[1] Adams, D. R. and Hedberg, L. I. 1996. Function Spaces and Potential Theory. Grundlehren der Mathematischen Wissenschaften, vol. 314. Berlin: Springer-Verlag.

[2] Adams, R. A. 1975. Sobolev Spaces. Pure and Applied Mathematics, vol. 65. New York/London: Academic Press, Harcourt Brace Jovanovich.

[3] Aikawa, H. and Essén, M. 1996. Potential Theory – Selected Topics. Lecture Notes in Mathematics, vol. 1633. Berlin: Springer-Verlag.

[4] Aikawa, H. and Ohtsuka, M. 1999. Extremal length of vector measures. Ann. Acad. Sci. Fenn. Math., 24(1), 61–88.Google Scholar

[5] Alexander, S., Kapovitch, V., and Petrunin, A.Alexandrov Geometry. Book in preparation. Draft available at www.math.psu.edu/petrunin/papers/alexandrov-geometry.

[6] Ambrosio, L. 1990. Metric space valued functions of bounded variation. Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4), 17(3), 439–478.Google Scholar

[7] Ambrosio, L. and Tilli, P. 2000. Selected Topics on “Analysis in Metric Spaces”. Appunti dei Corsi Tenuti da Docenti della Scuola, Scuola Normale Superiore, Pisa.

[8] Ambrosio, L. and Tilli, P. 2004. Topics on Analysis in Metric Spaces. Oxford Lecture Series in Mathematics and its Applications, vol. 25. Oxford: Oxford University Press.

[9] Ambrosio, L., Gigli, N., and Savaré, G. Bakry–Émery curvature-dimension condition and Riemannian Ricci curvature bounds. Preprint, 2012. Available at lanl.arxiv.org/abs/1209.5786.

[10] Ambrosio, L., Mondino, A., and Savaré, G. On the Bakry–Émery condition, the gradient estimates and the local-to-global property of RCD(K, N) metric measure spaces. Preprint, 2013. Available at lanl.arxiv.org/abs/1309.4664.

[11] Ambrosio, L., Di Marino, S., and Savaré, G. On the duality between p-modulus and probability measures. Preprint, 2013. Available at cvgmt.sns.it/paper/2271/.

[12] Ambrosio, L., Colombo, M., and Di Marino, S. Sobolev spaces in metric measure spaces: reflexivity and lower semicontinuity of slope. Preprint, 2012. Available at http://cvgmt.sns.it/media/doc/paper/2055.

[13] Ambrosio, L., Miranda, Jr., M., and Pallara, D. 2004. Special functions of bounded variation in doubling metric measure spaces, pp. 1–45 in: Calculus of Variations: Topics from the Mathematical Heritage of E. De Giorgi, Quad. Mat., vol. 14. Dept Math., Seconda Univ. Napoli.

[14] Ambrosio, L., Gigli, N., and Savaré, G. 2008. Gradient Flows in Metric Spaces and in the Space of Probability Measures. Second edn. Lectures in Mathematics, ETH Zürich. Basel: Birkhäuser Verlag.

[15] Ambrosio, L., Gigli, N., and Savaré, G. 2012. Heat flow and calculus on metric measure spaces with Ricci curvature bounded below – the compact case. Boll. Unione Mat. Ital. (9), 5(3), 575–629.Google Scholar

[16] Ambrosio, L., Gigli, N., and Savaré, G. 2013. Density of Lipschitz functions and equivalence of weak gradients in metric measure spaces. Rev. Mat. Iberoam., 29(3), 969–996.Google Scholar

[17] Armitage, D. H. and Gardiner, S. J. 2001. Classical Potential Theory. Springer Monographs in Mathematics. London: Springer-Verlag London Ltd.

[18] Assouad, P. 1983. Plongements lipschitziens dansRn. Bull. Soc. Math. France, 111(4), 429–448.Google Scholar

[19] Auscher, P., Coulhon, Th., and Grigor'yan, A. (eds.). 2003. Heat Kernels and Analysis on Manifolds, Graphs, and Metric Spaces. Contemporary Mathematics, vol. 338. Providence, RI: American Mathematical Society.

[20] Balogh, Z. M. and Buckley, S. M. 2005. Sphericalization and flattening. Conform. Geom. Dynam., 9, 76–101.Google Scholar

[21] Banach, S. 1955. Théorie des Óperations Linéaires. New York: Chelsea.

[22] Barlow, M. T., Bass, R. F., Kumagai, T., and Teplyaev, A. 2010. Uniqueness of Brownian motion on Sierpiński carpets. J. Eur. Math. Soc., 12(3), 655–701.Google Scholar

[23] Barvinok, A. 2002. A Course in Convexity. Graduate Studies in Mathematics, vol. 54. Providence, RI: American Mathematical Society.

[24] Bates, D. and Speight, G. 2013. Differentiability, porosity and doubling in metric measure spaces. Proc. Amer. Math. Soc., 141(3), 971–985.Google Scholar

[25] Baudoin, F. and Garofalo, N. 2011. Perelman's entropy and doubling property on Riemannian manifolds. J. Geom. Anal., 21(4), 1119–1131.Google Scholar

[26] Benyamini, Y. and Lindenstrauss, J. 2000. Geometric Nonlinear Functional Analysis, Volume I. Colloquium Publications, vol. 48. American Mathematical Society.

[27] Beurling, A. 1989. The Collected Works of Arne Beurling. Vol. 1. Contemporary Mathematicians. Boston, MA: Birkhäuser.

[28] Beurling, A. and Deny, J. 1959. Dirichlet spaces. Proc. Nat. Acad. Sci. USA, 45, 208–215.

[29] Billingsley, P. 1999. Convergence of Probability Measures. Second edn. Wiley Series in Probability and Statistics. New York: John Wiley & Sons.

[30] Bishop, C. and Hakobyan, H. Frequency of dimension distortion under quasisymmetric mappings. Preprint, 2013.

[31] Björn, A. and Björn, J. 2011. Nonlinear Potential Theory on Metric Spaces. EMS Tracts in Mathematics, vol. 17. Zürich: European Mathematical Society.

[32] Björn, A., Björn, J., and Shanmugalingam, N. 2003a. The Dirichlet problem for p-harmonic functions on metric spaces. J. Reine Angew. Math., 556, 173–203.Google Scholar

[33] Björn, A., Björn, J., and Shanmugalingam, N. 2003b. The Perron method for p-harmonic functions in metric spaces. J. Differential Equations, 195(2), 398–429.Google Scholar

[34] Björn, A., Björn, J., and Shanmugalingam, N. 2008. Quasicontinuity of Newton– Sobolev functions and density of Lipschitz functions on metric spaces. Houston J. Math., 34(4), 1197–1211.Google Scholar

[35] Björn, J. 2006. Wiener criterion for Cheeger p-harmonic functions on metric spaces, pp. 103–115 in: Adv. Stud. Pure Math., vol. 44. Tokyo: Mathematical Society of Japan.

[36] Björn, J., MacManus, P., and Shanmugalingam, N. 2001. Fat sets and pointwise boundary estimates for p-harmonic functions in metric spaces. J. Anal. Math., 85, 339–369.Google Scholar

[37] Bobkov, S. G. and Houdré, Ch. 1997. Some connections between isoperimetric and Sobolev-type inequalities. Mem. Amer. Math. Soc., 129(616).Google Scholar

[38] Bogachev, V. I. 1998. Gaussian Measures. Mathematical Surveys and Monographs, vol. 62. Providence, RI: American Mathematical Society.

[39] Bonk, M. 2006. Quasiconformal geometry of fractals, pp. 1349–1373 in: Proc. Int. Congress of Mathematicians. Vol. II. Zürich: European Mathematical Society.

[40] Bonk, M. and Kleiner, B. 2002. Quasisymmetric parametrizations of two-dimensional metric spheres. Invent. Math., 150(1), 127–183.Google Scholar

[41] Bonk, M. and Kleiner, B. 2005. Conformal dimension and Gromov hyperbolic groups with 2-sphere boundary. Geom. Topol., 9, 219–246.Google Scholar

[42] Bourdon, M. and Kleiner, B. 2013. Combinatorial modulus, the combinatorial Loewner property, and Coxeter groups. Groups Geom. Dyn., 7(1), 39–107.Google Scholar

[43] Bourdon, M. and Pajot, H. 1999. Poincaré inequalities and quasiconformal structure on the boundaries of some hyperbolic buildings. Proc. Amer. Math. Soc., 127(8), 2315–2324.Google Scholar

[44] Brelot, M. 1971. On Topologies and Boundaries in Potential Theory. Lecture Notes in Mathematics, vol. 175. Berlin: Springer-Verlag. Enlarged edition of a course of lectures delivered in 1966.

[45] Bridson, M. R. and Haefliger, A. 1999. Metric Spaces of Non-Positive Curvature. Grundlehren der Mathematischen Wissenschaften, vol. 319. Berlin: Springer-Verlag.

[46] Bruckner, A., Bruckner, J., and Thomson, B. 1997. Real Analysis. New Jersey: Prentice-Hall.

[47] Buckley, S. M. 1999. Is the maximal function of a Lipschitz function continuous?Ann. Acad. Sci. Fenn. Math., 24(2), 519–528.Google Scholar

[48] Buckley, S. M., Herron, D. A., and Xie, X. 2008. Metric space inversions, quasihyperbolic distance, and uniform spaces. Indiana Univ. Math. J., 57(2), 837–890.Google Scholar

[49] Burago, D., Burago, Yu., and Ivanov, S. 2001. A Course in Metric Geometry. Graduate Studies in Mathematics, vol. 33. Providence, RI: American Mathematical Society.

[50] Burago, Yu., Gromov, M., and Perel'man, G. 1992. A. D., Aleksandrov spaces with curvatures bounded below. Uspekhi Mat. Nauk, 47 3–51, 222.

[51] Buser, P. 1982. A note on the isoperimetric constant. Ann. Sci. École Norm. Sup. (4), 15, 213–230.Google Scholar

[52] Capogna, L., Danielli, D., Pauls, S. D., and Tyson, J. T. 2007. An Introduction to the Heisenberg Group and the Sub-Riemannian Isoperimetric Problem. Progress in Mathematics, vol. 259. Basel: Birkhäuser Verlag.

[53] Cheeger, J. 1999. Differentiability of Lipschitz functions on metric measure spaces. Geom. Funct. Anal., 9, 428–517.Google Scholar

[54] Cheeger, J. and Kleiner, B. 2006a. Generalized differential and bi-Lipschitz nonembedding in L1. C. R. Math. Acad. Sci. Paris, 343(5), 297–301.Google Scholar

[55] Cheeger, J. and Kleiner, B. 2006b. On the differentiability of Lipschitz maps from metric measure spaces to Banach spaces, pp. 129–152 in: Inspired by S. S. Chern, Nankai Tracts in Mathematics, vol. 11. Hackensack, NJ: World Science Publishers.

[56] Cheeger, J. and Kleiner, B. 2009. Differentiability of Lipschitz maps from metric measure spaces to Banach spaces with the Radon–Nikodým property. Geom. Funct. Anal., 19(4), 1017–1028.Google Scholar

[57] Cheeger, J. and Kleiner, B. 2010a. Differentiating maps into L1, and the geometry of BV functions. Ann. Math. (2), 171(2), 1347–1385.Google Scholar

[58] Cheeger, J. and Kleiner, B. 2010b. Metric differentiation, monotonicity and maps to L1. Invent. Math., 182(2), 335–370.Google Scholar

[59] Cheeger, J. and Kleiner, B. 2013. Realization of metric spaces as inverse limits, and bilipschitz embedding in L1. Geom. Funct. Anal., 23(1), 96–133.Google Scholar

[60] Cheeger, J., Kleiner, B., and Naor, A. 2011. Compression bounds for Lipschitz maps from the Heisenberg group to L1. Acta Math., 207(2), 291–373.Google Scholar

[61] Clarkson, J. A. 1936. Uniformly convex spaces. Trans. Amer. Math. Soc., 40, 396–414.Google Scholar

[62] Coifman, R. R. and de Guzmán, M. 1970/1971. Singular integrals and multipliers on homogeneous spaces. Rev. Univ. Mat. Argentina, 25, 137–143.Google Scholar

[63] Coifman, R. R. and Weiss, G. 1971. Analyse Harmonique Non-commutative sur Certains Espaces Homogènes. Lecture Notes in Mathematics, vol. 242. Berlin: Springer-Verlag.

[64] Coifman, R. R. and Weiss, G. 1977. Extensions of Hardy spaces and their use in analysis. Bull. Amer. Math. Soc., 83(4), 569–645.Google Scholar

[65] Colding, T. H. and Minicozzi, W. P., II. 1997. Harmonic functions on manifolds. Ann. Math. (2), 146, 725–747.Google Scholar

[66] Cucuringu, M. and Strichartz, R. S. 2008. Infinitesimal resistance metrics on Sierpinski gasket type fractals. Analysis (Munich), 28(3), 319–331.Google Scholar

[67] Danielli, D., Garofalo, N., and Marola, N. 2010. Local behavior of p-harmonic Green's functions in metric spaces. Potential Anal., 32(4), 343–362.Google Scholar

[68] David, G. and Semmes, S. 1990. Strong A∞ weights, Sobolev inequalities and quasiconformal mappings, pp. 101–111 in: Analysis and Partial Differential Equations. Lecture Notes in Pure and Applied Mathematics, vol. 122. Marcel Dekker.

[69] David, G. and Semmes, S. 1997. Fractured Fractals and Broken Dreams: Self-Similar Geometry Through Metric and Measure. Oxford Lecture Series in Mathematics and its Applications, vol. 7. Clarendon Press/Oxford University Press.

[70] Day, M. M. 1941. Reflexive Banach spaces not isomorphic to uniformly convex spaces. Bull. Amer. Math. Soc., 47, 313–317.Google Scholar

[71] DeJarnette, N. 2013. Self-improving Orlicz–Poincaré inequalities. Ph.D. thesis, University of Illinois at Urbana-Champaign.

[72] Deny, J. 1995. Formes et espaces de Dirichlet. pp. Exp. No. 187, 261–271 in: Séminaire Bourbaki, Vol. 5. Paris: Mathematical Society of France.

[73] Deny, J. and Lions, J. L. 1955. Les espaces du type de Beppo Levi. Ann. Inst. Fourier, Grenoble (5), 5, 305–370.Google Scholar

[74] Diestel, J. 1984. Sequences and Series in Banach Spaces. Graduate Texts in Mathematics, vol. 92. New York: Springer-Verlag.

[75] Diestel, J. and Uhl, J. J. 1977. Vector Measures. Mathematical Surveys, vol. 15. Providence, R.I.: American Mathematical Society. With a foreword by B. J. Pettis.

[76] Doob, J. L. 1984. Classical Potential Theory and its Probabilistic Counterpart. Grundlehren der Mathematischen Wissenschaften, vol. 262. New York: Springer-Verlag.

[77] Dunford, N. and Schwartz, J. T. 1988. Linear Operators. Part I. Wiley Classics Library. New York: John Wiley & Sons.

[78] Durand-Cartagena, E. and Shanmugalingam, N. Geometric characterizations of ∞-Poincaré and p-Poincaré inequalities in the metric setting. Preprint, 2014.

[79] Durand-Cartagena, E., Jaramillo, J. A., and Shanmugalingam, N. 2012. The ∞-Poincaré inequality in metric measure spaces. Michigan Math. J., 61(1), 63–85.Google Scholar

[80] Durand-Cartagena, E., Shanmugalingam, N., and Williams, A. 2012. p-Poincaré inequality versus ∞-Poincaré inequality: some counterexamples. Math. Z., 271(1–2), 447–467.Google Scholar

[81] Evans, L. C. and Gariepy, R. F. 1992. Measure Theory and Fine Properties of Functions. Studies in Advanced Mathematics. Boca Raton, FL: CRC Press.

[82] Fabes, E. B., Kenig, C. E., and Serapioni, R. 1982. The local regularity of solutions to degenerate elliptic equations. Comm. PDE, 7, 77–116.Google Scholar

[83] Federer, H. 1969. Geometric Measure Theory. Die Grundlehren der mathematischen Wissenschaften, vol. 153. New York: Springer-Verlag.

[84] Federer, H. and Ziemer, W. P. 1972/73. The Lebesgue set of a function whose distribution derivatives are pth power summable. Indiana Univ. Math. J., 22, 139–158.Google Scholar

[85] Fitzsimmons, P. J., Hambly, B. M., and Kumagai, T. 1994. Transition density estimates for Brownian motion on affine nested fractals. Comm. Math. Phys., 165(3), 595–620.Google Scholar

[86] Folland, G. B. 1984. Real Analysis. Pure and Applied Mathematics. John Wiley & Sons.

[87] Franchi, B., Hajłasz, P., and Koskela, P. 1999. Definitions of Sobolev classes on metric spaces. Ann. Inst. Fourier (Grenoble), 49(6), 1903–1924.Google Scholar

[88] Fréchet, M. 1909–10. Les dimensions d'un ensemble abstrait. Math. Ann., 68, 145–168.Google Scholar

[89] Fuglede, B. 1957. Extremal length and functional completion. Acta Math., 98, 171–219.Google Scholar

[90] Fukushima, M., Ōshima, Y., and Takeda, M. 1994. Dirichlet Forms and Symmetric Markov Processes. Berlin: Walter de Gruyter & Co.

[91] Ghys, E. and de la Harpe, P. 1990. Sur les Groupes Hyperboliques d'après Mikhael Gromov. Progress in Mathematics. Boston/Basel/Berlin: Birkhäuser.

[92] Giaquinta, M. and Giusti, E. 1982. On the regularity of the minima of variational integrals. Acta Math., 148, 31–46.Google Scholar

[93] Giaquinta, M. and Giusti, E. 1984. Quasiminima. Ann. Inst. H. Poincaré Anal. Non Linéaire, 1(2), 79–107.

[94] Gigli, N., Kuwada, K., and Ohta, S.-I. 2013. Heat flow on Alexandrov spaces. Comm. Pure Appl. Math., 66(3), 307–331.Google Scholar

[95] Giusti, E. 1969. Precisazione delle funzioni di H1, p e singolarità delle soluzioni deboli di sistemi ellittici non lineari. Boll. Un. Mat. Ital. (4), 2, 71–76.Google Scholar

[96] Gol'dshtein, V. and Troyanov, M. 2001. Axiomatic theory of Sobolev spaces. Expo. Math., 19(4), 289–336.Google Scholar

[97] Gol'dshtein, V. and Troyanov, M. 2002a. Axiomatic Sobolev spaces on metric spaces. pp. 333–343 in: Proc. Conf. on Function Spaces, Interpolation Theory and Related Topics (Lund, 2000). Berlin: de Gruyter.Google Scholar

[98] Gol'dshtein, V. and Troyanov, M. 2002b. Capacities in metric spaces. Integral Eq. Operator Theory, 44(2), 212–242.Google Scholar

[99] Gong, J. The Lip–lip condition on metric measure spaces. Preprint, 2012. Available at arxiv.org/abs/1208.2869.

[100] Gong, J. Measurable differentiable structures on doubling metric spaces. Preprint, 2012. Available at arxiv.org/abs/1110.4279.

[101] Gong, J. 2012 Rigidity of derivations in the plane and in metric measure spaces. Illinois J. Math., 56(4), 1109–1147.Google Scholar

[102] Gong, J. 2007. Derivatives and currents on metric (measure) spaces. Real Anal. Exchange, 217–223.Google Scholar

[103] Grigor'yan, A. 1995. Heat kernel of a noncompact Riemannian manifold, pp. 239–263 in: Stochastic Analysis (Ithaca, NY, 1993), Proc. Sympos. Pure Math., vol. 57. Providence, RI: American Mathematical Society.

[104] Grigor'yan, A. 1999. Analytic and geometric background of recurrence and non-explosion of Brownian motion on Riemannian manifolds. Bull. Amer. Math. Soc. (NS), 36(2), 135–249.Google Scholar

[105] Gromov, M. 1987. Hyperbolic groups, pp. 75–265 in: Essays in Group Theory. MSRI Publications, Springer-Verlag.

[106] Gromov, M. 1996. Carnot–Carathéodory spaces seen from within, pp. 79–323 in: Sub-Riemannian Geometry, Progress in Mathematics, vol. 144. Basel: Birkhäuser.

[107] Gromov, M. 1999. Metric Structures for Riemannian and Non-Riemannian spaces. Progress in Mathematics, vol. 152. Boston, MA: Birkhäuser Boston. Based on the 1981 French original, with appendices by M., Katz, P., Pansu, and S., Semmes; translated from the French by Sean Michael Bates.

[108] Hajłasz, P. 1996. Sobolev spaces on an arbitrary metric space. Potential Anal., 5, 403–415.Google Scholar

[109] Hajłasz, P. 2003. Sobolev spaces on metric-measure spaces, pp. 173–218 in: Proc. Conf. on Heat Kernels and Analysis on Manifolds, Graphs, and Metric Spaces (Paris, 2002). Contemp. Math., vol. 338. Providence, RI: American Mathematical Society.Google Scholar

[110] Hajłasz, P. 2007. Sobolev mappings: Lipschitz density is not a bi-Lipschitz invariant of the target. Geom. Funct. Anal., 17(2), 435–467.Google Scholar

[111] Hajłasz, P. 2009a. Density of Lipschitz mappings in the class of Sobolev mappings between metric spaces. Math. Ann., 343(4), 801–823.Google Scholar

[112] Hajłasz, P. 2009b. Sobolev mappings between manifolds and metric spaces, pp. 185–222 in: Sobolev Spaces in Mathematics. Vol. I. Int. Math. Ser. (NY), vol. 8. New York: Springer.

[113] Hajłasz, P. and Koskela, P. 1995. Sobolev meets Poincaré. C. R. Acad. Sci. Paris Sér. I Math., 320, 1211–1215.Google Scholar

[114] Hajłasz, P. and Koskela, P. 2000. Sobolev met Poincaré. Mem. Amer. Math. Soc., 145(688).Google Scholar

[115] Hakobyan, H. 2010. Conformal dimension: Cantor sets and Fuglede modulus. Int. Math. Res. Not. IMRN, 87–111.Google Scholar

[116] Hambly, B. M. and Kumagai, T. 1999. Transition density estimates for diffusion processes on post critically finite self-similar fractals. Proc. London Math. Soc. (3), 78(2), 431–458.Google Scholar

[117] Hanson, B. and Heinonen, J. 2000. An n-dimensional space that admits a Poincaré inequality but has no manifold points. Proc. Amer. Math. Soc., 128(11), 3379–3390.Google Scholar

[118] Hebey, E. 1999. Nonlinear Analysis on Manifolds: Sobolev Spaces and Inequalities. Courant Lecture Notes in Mathematics, vol. 5. New York: Courant Institute of Mathematical Sciences.

[119] Heinonen, J. 1995. A capacity estimate on Carnot groups. Bull. Sci. Math., 119, 475–484.Google Scholar

[120] Heinonen, J. 2001. Lectures on Analysis on Metric Spaces. New York: Springer-Verlag.

[121] Heinonen, J. 2003. Geometric embeddings of metric spaces. Report, University of Jyväskylä Department of Mathematics and Statistics, vol. 90. University of Jyväskylä.

[122] Heinonen, J. 2007. Nonsmooth calculus. Bull. Amer. Math. Soc. (NS), 44(2), 163–232.

[123] Heinonen, J. and Koskela, P. 1995. Definitions of quasiconformality. Invent. Math., 120, 61–79.Google Scholar

[124] Heinonen, J. and Koskela, P. 1996. From local to global in quasiconformal structures. Proc. Nat. Acad. Sci. USA, 93, 554–556.Google Scholar

[125] Heinonen, J. and Koskela, P. 1998. Quasiconformal maps in metric spaces with controlled geometry. Acta Math., 181, 1–61.Google Scholar

[126] Heinonen, J. and Koskela, P. 1999. A note on Lipschitz functions, upper gradients, and the Poincaré inequality. New Zealand J. Math., 28, 37–42.Google Scholar

[127] Heinonen, J. and Wu, J.-M. 2010. Quasisymmetric nonparametrization and spaces associated with the Whitehead continuum. Geom. Topol., 14(2), 773–798.Google Scholar

[128] Heinonen, J., Kilpeläinen, T., and Martio, O. 1993. Nonlinear Potential Theory of Degenerate Elliptic Equations. Oxford Science Publications. New York: The Clarendon Press, Oxford University Press.

[129] Heinonen, J., Koskela, P., Shanmugalingam, N., and Tyson, J. T. 2001. Sobolev classes of Banach space-valued functions and quasiconformal mappings. J. Anal. Math., 85, 87–139.Google Scholar

[130] Herman, P. E., Peirone, R., and Strichartz, R. S. 2004. p-energy and p-harmonic functions on Sierpinski gasket type fractals. Potential Anal., 20(2), 125–148.Google Scholar

[131] Herron, D. A. Gromov–Hausdorff distance for pointed metric spaces. Preprint, 2011.

[132] Herron, D. A. 2011. Uniform metric spaces, annular quasiconvexity and pointed tangent spaces. Math. Scand., 108(1), 115–145.Google Scholar

[133] Herron, D. A., Shanmugalingam, N., and Xie, X. 2008. Uniformity from Gromov hyperbolicity. Illinois J. Math., 52(4), 1065–1109.Google Scholar

[134] Hesse, J. 1975. p-extremal length and p-measurable curve families. Proc. Amer. Math. Soc., 53(2), 356–360.Google Scholar

[135] Hewitt, E. and Stromberg, K. 1965. Real and Abstract Analysis. A Modern Treatment of the Theory of Functions of a Real Variable. New York: Springer-Verlag.

[136] Hildebrandt, T. H. 1953. Integration in abstract spaces. Bull. Amer. Math. Soc., 59, 111–139.Google Scholar

[137] Holopainen, I. 1990. Nonlinear potential theory and quasiregular mappings on Riemannian manifolds. Ann. Acad. Sci. Fenn. Ser. A I Math. Dissertationes, 45.Google Scholar

[138] Jacobs, K. 1978. Measure and Integral. New York: Academic Press, Harcourt Brace Jovanovich.

[139] Järvenpää, E., Järvenpää, M., Rogovin, K., Rogovin, S., and Shanmugalingam, N. 2007. Measurability of equivalence classes and MECp-property in metric spaces. Rev. Mat. Iberoam., 23(3), 811–830.Google Scholar

[140] Jiang, R. 2012. Lipschitz continuity of solutions of Poisson equations in metric measure spaces. Potential Anal., 37(3), 281–301.Google Scholar

[141] Jiang, R. and Koskela, P. 2012. Isoperimetric inequality from the Poisson equation via curvature. Comm. Pure Appl. Math., 65(8), 1145–1168.Google Scholar

[142] John, F. 1948. Extremum problems with inequalities as subsidiary conditions, pp. 187–204 in: Studies and Essays Presented to R. Courant on his 60th Birthday, January 8, 1948. New York: Interscience.

[143] Johnson, W. B., Lindenstrauss, J., and Schechtman, G. 1986. Extensions of Lipschitz maps into Banach spaces. Israel J. Math., 54(2), 129–138.Google Scholar

[144] Kajino, N. 2012a. Heat kernel asymptotics for the measurable Riemannian structure on the Sierpinski gasket. Potential Anal., 36(1), 67–115.Google Scholar

[145] Kajino, N. 2012b. Time changes of local Dirichlet spaces by energy measures of harmonic functions. Forum Math., 24(2), 339–363.Google Scholar

[146] Kapovich, I. and Benakli, N. 2002. Boundaries of hyperbolic groups, pp. 39–93 in: Combinatorial and Geometric Group Theory, Contemp. Math., vol. 296. Providence, RI: American Mathematical Society.

[147] Kapovitch, V. 2007. Perelman's stability theorem. pp. 103–136 in: Surveys in Differential Geometry, vol. 11. Somerville, MA: Int. Press.

[148] Karak, N. Removable sets for Orlicz–Sobolev spaces. Preprint, 2013.

[149] Kechris, A. S. 1995. Classical Descriptive Set Theory. Graduate Texts in Mathematics, vol. 156. New York: Springer-Verlag.

[150] Keith, S. 2003. Modulus and the Poincaré inequality on metric measure spaces. Math. Z., 245(2), 255–292.Google Scholar

[151] Keith, S. 2004a. A differentiable structure for metric measure spaces. Adv. Math., 183(2), 271–315.Google Scholar

[152] Keith, S. 2004b. Measurable differentiable structures and the Poincaré inequality. Indiana Univ. Math. J., 53(4), 1127–1150.Google Scholar

[153] Keith, S. and Zhong, X. 2008. The Poincaré inequality is an open ended condition. Ann. Math. (2), 167(2), 575–599.Google Scholar

[154] Kigami, J. 1994. Effective resistances for harmonic structures on p.c.f. self-similar sets. Math. Proc. Cambridge Phil. Soc., 115(2), 291–303.Google Scholar

[155] Kigami, J. 2001. Analysis on Fractals. Cambridge Tracts in Mathematics, vol. 143. Cambridge: Cambridge University Press.

[156] Kigami, J., Strichartz, R. S., and Walker, K. C. 2001. Constructing a Laplacian on the diamond fractal. Experimental Math., 10(3), 437–448.Google Scholar

[157] Kinnunen, J. and Latvala, V. 2002. Lebesgue points for Sobolev functions on metric spaces. Rev. Mat. Iberoam., 18(3), 685–700.Google Scholar

[158] Kinnunen, J. and Shanmugalingam, N. 2001. Regularity of quasi-minimizers on metric spaces. Manuscripta Math., 105(3), 401–423.Google Scholar

[159] Kinnunen, J. and Shanmugalingam, N. 2006. Polar sets on metric spaces. Trans. Amer. Math. Soc., 358(1), 11–37.Google Scholar

[160] Kinnunen, J., Korte, R., Shanmugalingam, N., and Tuominen, Heli. 2008. Lebesgue points and capacities via the boxing inequality in metric spaces. Indiana Univ. Math. J., 57(1), 401–430.Google Scholar

[161] Kinnunen, J., Korte, R., Lorent, A., and Shanmugalingam, N. 2013. Regularity of sets with quasiminimal boundary surfaces in metric spaces. J. Geom. Anal., 23(4), 1607–1640.Google Scholar

[162] Kleiner, B. 2006. The asymptotic geometry of negatively curved spaces: uniformization, geometrization and rigidity, pp. 743–768 in: International Congress of Mathematicians, Vol. II. Zürich: European Mathematical Society.

[163] Kleiner, B. and Mackay, J. 2011. Differentiable structures on metric measure spaces: a primer. Preprint. Available at arxiv.org/abs/1108.1324.

[164] Korevaar, N. J. and Schoen, R. M. 1993. Sobolev spaces and harmonic maps for metric space targets. Comm. Anal. Geom., 1, 561–659.Google Scholar

[165] Korte, R. 2007. Geometric implications of the Poincaré inequality. Results Math., 50(1–2), 93–107.Google Scholar

[166] Korte, R., Lahti, P., and Shanmugalingam, N. Semmes family of curves and a characterization of functions of bounded variation in terms of curves. Preprint, 2013. Available at cvgmt.sns.it/paper/2229/.

[167] Koskela, P. 1999. Removable sets for Sobolev spaces. Ark. Mat., 37(2), 291–304.Google Scholar

[168] Koskela, P. and MacManus, P. 1998. Quasiconformal mappings and Sobolev spaces. Studia Math., 131, 1–17.Google Scholar

[169] Koskela, P. and Saksman, E. 2008. Pointwise characterizations of Hardy–Sobolev functions. Math. Res. Lett., 15(4), 727–744.Google Scholar

[170] Koskela, P. and Zhou, Y. 2012. Geometry and analysis of Dirichlet forms. Adv. Math., 231(5), 2755–2801.Google Scholar

[171] Koskela, P., Rajala, K., and Shanmugalingam, N. 2003. Lipschitz continuity of Cheeger-harmonic functions in metric measure spaces. J. Funct. Anal., 202(1), 147–173.Google Scholar

[172] Koskela, P., Shanmugalingam, N., and Tyson, J. T. 2004. Dirichlet forms, Poincaré inequalities, and the Sobolev spaces of Korevaar and Schoen. Potential Anal., 21(3), 241–262.Google Scholar

[173] Koskela, P., Shanmugalingam, N., and Zhou, Y. 2012. L∞-variational problem associated to Dirichlet forms. Math. Res. Lett., 19(6), 1263–1275.

[174] Kumagai, T. 1993. Regularity, closedness and spectral dimensions of the Dirichlet forms on PCF. self-similar sets. J. Math. Kyoto Univ., 33(3), 765–786.Google Scholar

[175] Kuratowski, C. 1935. Quelques problèmes concernant les espaces métriques non-séparables. Fund. Math., 25, 534–545.Google Scholar

[176] Kuwae, K., Machigashira, Y., and Shioya, T. 2001. Sobolev spaces, Laplacian, and heat kernel on Alexandrov spaces. Math. Z., 238(2), 269–316.Google Scholar

[177] Laakso, T. J. 2000. Ahlfors Q-regular spaces with arbitrary Q > 1 admitting weak Poincaré inequality. Geom. Funct. Anal., 10(1), 111–123.Google Scholar

[178] Ladyzhenskaya, O. A. and Ural'tseva, N. N. 1984. Estimates of max |ux| for solutions of quasilinear elliptic and parabolic equations of general type, and some existence theorems. Zap. Nauchn. Sem. Leningrad. Otdel. Mat. Inst. Steklov. (LOMI), 138, 90–107.Google Scholar

[179] Lang, U. and Schlichenmaier, T. 2005. Nagata dimension, quasisymmetric embeddings, and Lipschitz extensions. Int. Math. Res. Not., 3625–3655.Google Scholar

[180] Lang, U., Pavlović, B., and Schroeder, V. 2000. Extensions of Lipschitz maps into Hadamard spaces. Geom. Funct. Anal., 10(6), 1527–1553.Google Scholar

[181] Ledoux, M. and Talagrand, M. 1991. Probability in Banach Spaces. Ergebnisse der Mathematik und ihrer Grenzgebiete (3), vol. 23. Berlin: Springer-Verlag.

[182] Lee, J. R. and Naor, A. 2005. Extending Lipschitz functions via random metric partitions. Invent. Math., 160(1), 59–95.Google Scholar

[183] Levi, B. 1906. Sul principio di Dirichlet. Rend. Circ. Mat. Palermo, 22, 293–359.Google Scholar

[184] Li, P. and Tam, L.-F. 1995. Green's functions, harmonic functions, and volume comparison. J. Differential Geom., 41(2), 277–318.Google Scholar

[185] Li, S. 2014. Coarse differentiation and quantitative nonembeddability for Carnot groups. J. Funct. Anal., 266(7), 4616–4704.Google Scholar

[186] Li, X. and Shanmugalingam, N. Preservation of bounded geometry under sphericalization and flattening. Preprint 2013. Report No. IML-1314f-16, Institut Mittag-Leffler preprint series. Available at www.mittag-leffler.se/preprints/files/IML-1314f-16.pdf. Indiana. Math J., to appear.

[187] Liu, Y., Lu, G., and Wheeden, R. L. 2002. Some equivalent definitions of high order Sobolev spaces on stratified groups and generalizations to metric spaces. Math. Ann., 323(1), 157–174.Google Scholar

[188] Lott, J. and Villani, C. 2007. Weak curvature conditions and functional inequalities. J. Funct. Anal., 245(1), 311–333.Google Scholar

[189] Lott, J. and Villani, C. 2009. Ricci curvature for metric-measure spaces via optimal transport. Ann. Math. (2), 169(3), 903–991.Google Scholar

[190] Luukkainen, J. and Saksman, E. 1998. Every complete doubling metric space carries a doubling measure. Proc. Amer. Math. Soc., 126, 531–534.Google Scholar

[191] Mackay, J. M. 2010. Spaces and groups with conformal dimension greater than one. Duke Math. J., 153(2), 211–227.Google Scholar

[192] Mackay, J. M., Tyson, J. T., and Wildrick, K. 2013. Modulus and Poincaré inequalities on non-self-similar Sierpiński carpets. Geom. Funct. Anal., 23(3), 985–1034.Google Scholar

[193] Malý, J. and Ziemer, W. P. 1997. Fine Regularity of Solutions of Elliptic Partial Differential Equations. Mathematical Surveys and Monographs, vol. 51. Providence, RI: American Mathematical Society.

[194] Malý, L. 2013. Minimal weak upper gradients in Newtonian spaces based on quasi-Banach function lattices. Ann. Acad. Sci. Fenn. Math., 38(2), 727–745.Google Scholar

[195] Marola, N., Miranda, M., Jr., and Shanmugalingam, N. Boundary measures, generalized Gauss–Green formulas and the mean value property in metric measure spaces. Available at cvgmt.sns.it/paper/2129. Rev. Mat. lberoamericana, to appear.

[196] Mattila, P. 1973. Integration in a space of measures. Ann. Acad. Sci. Fenn. Ser. A I, 1–37.Google Scholar

[197] Mattila, P. 1995. Geometry of Sets and Measures in Euclidean Spaces. Cambridge Studies in Advanced Mathematics, vol. 44. Cambridge: Cambridge University Press.

[198] Maz'ya, V. G. 1960. Classes of domains and imbedding theorems for function spaces. Soviet Math. Dokl., 1, 882–885.Google Scholar

[199] Maz'ya, V. G. 1964. On the theory of the higher-dimensional Schrödinger operator. Izv. Akad. Nauk SSSR Ser. Mat., 28, 1145–1172.Google Scholar

[200] Maz'ya, V. G. 1970. Classes of sets and measures that are connected with imbedding theorems. Izdat. “Nauka”, Moscow, pp. 142–159, 246.

[201] Maz'ya, V. G. 1975. The summability of functions belonging to Sobolev spaces. Izdat. Leningrad. Univ., Leningrad, pp. 66–98.

[202] Maz'ya, V. G. 1985. Sobolev Spaces. Berlin: Springer-Verlag. Translated from the Russian by T. O. Shaposhnikova.

[203] McShane, E. J. 1934. Extension of range of functions. Bull. Amer. Math. Soc., 40, 837–842.Google Scholar

[204] McShane, E. J. 1944. Integration. Princeton, NJ: Princeton University Press.

[205] McShane, E. J. 1950. Linear functionals on certain Banach spaces. Proc. Amer. Math. Soc., 1, 402–408.Google Scholar

[206] Megginson, R. E. 1998. An Introduction to Banach Space Theory. Graduate Texts in Mathematics, vol. 183. New York: Springer-Verlag.

[207] Meyers, N. and Serrin, J. 1964. H = W. Proc. Nat. Acad. Sci. USA, 51, 1055–1056.

[208] Milman, V. D. and Schechtman, G. 1986. Asymptotic Theory of Finite-Dimensional Normed Spaces. Lecture Notes in Mathematics, vol. 1200. Berlin: Springer-Verlag. With an appendix by M. Gromov.

[209] Miranda, M., Jr. 2003. Functions of bounded variation on “good” metric spaces. J. Math. Pures Appl. (9), 82(8), 975–1004.Google Scholar

[210] Mitchell, J. 1985. On Carnot–Carathéodory metrics. J. Differential Geom., 21, 35–45.Google Scholar

[211] Montgomery, R. 2002. A Tour of Subriemannian Geometries, their Geodesics and Applications. Mathematical Surveys and Monographs, vol. 91. Providence, RI: American Mathematical Society.

[212] Morrey, C. B. 1966. Multiple Integrals in the Calculus of Variations. Berlin: Springer-Verlag.

[213] Muckenhoupt, B. 1972. Weighted norm inequalities for the Hardy maximal function. Trans. Amer. Math. Soc., 165, 207–226.Google Scholar

[214] Munkres, J. R. 1975. Topology: A First Course. Englewood Cliffs, NJ: Prentice-Hall.

[215] Nadler, S. B. 1978. Hyperspaces of Sets. Monographs and Textbooks in Pure and Applied Mathematics, vol. 49. New York: Marcel Dekker.

[216] Naor, A. 2010. L1 embeddings of the Heisenberg group and fast estimation of graph isoperimetry, pp. 1549–1575 in: Proc. Int. Congress of Mathematicians, Vol. III. New Delhi: Hindustan Book Agency.

[217] Nazarov, F., Treil, S., and Volberg, A. 1998. Weak type estimates and Cotlar inequalities for Calderón–Zygmund operators on nonhomogeneous spaces. Int. Math. Res. Not., 463–487.Google Scholar

[218] Nazarov, F., Treil, S., and Volberg, A. >2003. The Tb-theorem on non-homogeneous spaces. Acta Math., 190(2), 151–239.Google Scholar

[219] Nikodym, O. M. 1933. Sur une classe de fonctions considérées dans problème de Dirichlet. Fund. Math., 21, 129–150.Google Scholar

[220] Ohtsuka, M. 2003. Extremal Length and Precise Functions. GAKUTO International Series. Mathematical Sciences and Applications, vol. 19. Tokyo: Gakkōtosho. With a preface by Fumi-Yuki Maeda.

[221] Oxtoby, J. C. and Ulam, S. M. 1939. On the existence of a measure invariant under a transformation. Ann. Math. (2), 40, 560–566.Google Scholar

[222] Pankka, P. and Wu, J.-M. 2014. Geometry and quasisymmetric parametrization of Semmes spaces. Rev. Mat. Iberoamericana, 30(4), 893–960.Google Scholar

[223] Pansu, P. 1989a. Dimension conforme et sphère à l'infini des variétés à courbure négative. Ann. Acad. Sci. Fenn. Ser. A I Math., 14, 177–212.Google Scholar

[224] Pansu, P. 1989b. Métriques de Carnot–Carathéodory et quasiisométries des espaces symétriques de rang un. Ann. Math. (2), 129, 1–60.Google Scholar

[225] Perelman, G. 1995. Spaces with curvature bounded below, pp. 517–525 in: Proc. Int. Congress of Mathematicians, Vols. 1, 2 (Zürich, 1994). Basel: Birkhäuser.

[226] Rademacher, H. 1919. Über partielle und totale Differenzierbarkeit von Funktionen mehrerer Variabeln und über die Transformation der Doppelintegrale. Math. Ann., 79(4), 340–359.Google Scholar

[227] Rajala, K. 2005. Surface families and boundary behavior of quasiregular mappings. Illinois J. Math., 49(4), 1145–1153.Google Scholar

[228] Rajala, K. and Wenger, S. 2013. An upper gradient approach to weakly differentiable cochains. J. Math. Pures Appl., 100, 868–906.Google Scholar

[229] Rauch, H. E. 1956. Harmonic and analytic functions of several variables and the maximal theorem of Hardy and Littlewood. Can. J. Math., 8, 171–183.Google Scholar

[230] Reimann, H. M. 1989. An estimate for pseudoconformal capacities on the sphere. Ann. Acad. Sci. Fenn. Ser. A I Math., 14, 315–324.Google Scholar

[231] Reshetnyak, Yu. G. 1967. Space Mappings with Bounded Distortion. Sibirsk. Mat. Z., 8, 629–659.Google Scholar

[232] Reshetnyak, Yu. G. 1989. Space Mappings with Bounded Distortion. Translations of Mathematical Monographs, vol. 73. American Mathematical Society. Translated from the Russian by H. H. McFaden.

[233] Reshetnyak, Yu. G. 1997. Sobolev classes of functions with values in a metric space. Sibirsk. Mat. Zh., 38, 657–675.Google Scholar

[234] Rickman, S. 1993. Quasiregular Mappings. Berlin: Springer-Verlag.

[235] Rogers, C. A. 1970. Hausdorff Measures. London: Cambridge University Press.

[236] Royden, H. L. 1988. Real Analysis. Third edn. Macmillan Publ. Co.

[237] Rudin, W. 1987. Real and Complex Analysis. Third edn. New York: McGraw-Hill.

[238] Rudin, W. 1991. Functional Analysis. Second edn. New York: McGraw-Hill.

[239] Saksman, E. 1999. Remarks on the nonexistence of doubling measures. Ann. Acad. Sci. Fenn. Ser. A I Math., 24(1), 155–163.Google Scholar

[240] Saloff-Coste, L. 2002. Aspects of Sobolev-type Inequalities. London Mathematical Society Lecture Note Series, vol. 289. Cambridge: Cambridge University Press.

[241] Savaré, G. 2014. Self-improvement of the Bakry–Émery condition and Wasserstein contraction of the heat flow in RCD(K, ∞) metric measure spaces. Discrete Contin. Dynam. Syst., 34(4), 1641–1661.Google Scholar

[242] Schechter, M. 2002. Principles of Functional Analysis. Second edn. Graduate Studies in Mathematics, vol. 36. Providence, RI: American Mathematical Society.

[243] Schwartz, L. 1973. Radon Measures on Arbitrary Topological Spaces and Cylindrical Measures. Tata Institute of Fundamental Research Studies in Mathematics, no. 6. London: Published for the Tata Institute of Fundamental Research, Bombay by Oxford University Press.

[244] Semmes, S. 1996a. Finding curves on general spaces through quantitative topology, with applications to Sobolev and Poincaré inequalities. Selecta Math., 2, 155–295.Google Scholar

[245] Semmes, S. 1996b. Good metric spaces without good parameterizations. Rev. Mat. Iberoam., 12, 187–275.Google Scholar

[246] Semmes, S. 1996c. On the nonexistence of bi-Lipschitz parameterizations and geometric problems about A∞-weights. Rev. Mat. Iberoam., 12, 337–410.Google Scholar

[247] Shanmugalingam, N. 1999. Newtonian spaces: an extension of Sobolev spaces to metric measure spaces. Ph.D. thesis, University of Michigan.

[248] Shanmugalingam, N. 2000. Newtonian spaces: an extension of Sobolev spaces to metric measure spaces. Rev. Mat. Iberoam., 16(2), 243–279.Google Scholar

[249] Shanmugalingam, N. 2001. Harmonic functions on metric spaces. Illinois J. Math., 45(3), 1021–1050.

[250] Shanmugalingam, N. 2009. A universality property of Sobolev spaces in metric measure spaces, pp. 345–359 in: Sobolev Spaces in Mathematics. Vol. I. International Mathematics Series (NY), vol. 8. New York: Springer.

[251] Shiryaev, A. N. 1996. Probability. Second edn. Graduate Texts in Mathematics, vol. 95. New York: Springer-Verlag. Translated from the first (1980) Russian edition by R. P. Boas.

[252] Smith, K. T. 1956. A generalization of an inequality of Hardy and Littlewood. Can. J. Math., 8, 157–170.Google Scholar

[253] Sobolev, S. L. 1936. On some estimates relating to families of functions having derivatives that are square integrable. Dokl. Akad. Nauk SSSR, 1, 267–270. (In Russian).Google Scholar

[254] Sobolev, S. L. 1938. On a theorem in functional analysis. Math. Sb., 4, 471–497. (In Russian.)Google Scholar

[255] Sobolev, S. L. 1950. Some Applications of Functional Analysis in Mathematical Physics. Izdat. Leningrad. Gos. Univ., Leningrad. (In Russian).

[256] Sobolev, S. L. 1991. Some Applications of Functional Analysis in Mathematical Physics. Translations of Mathematical Monographs, vol. 90. Providence, RI: American Mathematical Society. Translated from the third Russian edition by Harold H., McFaden. With comments by V. P., Palamodov.

[257] Stein, E. M. 1993. Harmonic Analysis: Real-Variable Methods, Orthogonality, and Oscillatory Integrals. Princeton Mathematical Series. Princeton, NJ: Princeton University Press.

[258] Strichartz, R. S. 1998. Fractals in the large. Can. J. Math., 50(3), 638–657.Google Scholar

[259] Strichartz, R. S. 1999a. Analysis on fractals. Not. Amer. Math. Soc., 46(10), 1199–1208.Google Scholar

[260] Strichartz, R. S. 1999b. Some properties of Laplacians on fractals. J. Funct. Anal., 164(2), 181–208.Google Scholar

[261] Strichartz, R. S. 2001. The Laplacian on the Sierpinski gasket via the method of averages.Pacific J. Math., 201(1), 241–256.Google Scholar

[262] Strichartz, R. S. 2002. Harmonic mappings of the Sierpinski gasket to the circle. Proc. Amer. Math. Soc., 130(3), 805–817.Google Scholar

[263] Strichartz, R. S. 2003. Function spaces on fractals. J. Funct. Anal., 198(1), 43–83.Google Scholar

[264] Sturm, K.-Th. 2005. Generalized Ricci bounds and convergence of metric measure spaces. C. R. Math. Acad. Sci. Paris, 340(3), 235–238.Google Scholar

[265] Sturm, K.-Th. 2006a. A curvature–dimension condition for metric measure spaces. C. R. Math. Acad. Sci. Paris, 342(3), 197–200.Google Scholar

[266] Sturm, K.-Th. 2006b. On the geometry of metric measure spaces. II. Acta Math., 196(1), 133–177.Google Scholar

[267] Tolsa, X. 1998. Cotlar's inequality without the doubling condition and existence of principal values for the Cauchy integral of measures. J. Reine Angew. Math., 502, 199–235.Google Scholar

[268] Tolsa, X. 1999. L2-boundedness of the Cauchy integral operator for continuous measures. Duke Math. J., 98(2), 269–304.Google Scholar

[269] Tonelli, L. 1926. Sulla quadratura delle superficie. Atti Reale Accad. Lincei, 3, 633–638.Google Scholar

[270] Tuominen, H. 2004. Orlicz–Sobolev spaces on metric measure spaces. Ann. Acad. Sci. Fenn. Math. Diss., 135, 1–86.Google Scholar

[271] Tyson, J. T. 1998. Quasiconformality and quasisymmetry in metric measure spaces. Ann. Acad. Sci. Fenn. Ser. A I Math., 23, 525–548.Google Scholar

[272] Tyson, J. T. 1999. Geometric and analytic applications of a generalized definition of the conformal modulus. Ph.D. thesis, University of Michigan.

[273] Väisälä, J. 1971. Lectures on n-Dimensional Quasiconformal Mappings. Lecture Notes in Mathematics, vol. 229. Berlin: Springer-Verlag.

[274] Varopoulos, N. 1987. Fonctions harmoniques sur les groupes de Lie. C. R. Acad. Sci. Paris Sér. I Math., 304, 519–521.Google Scholar

[275] Verdera, J. 2002. The fall of the doubling condition in Calderón–Zygmund theory, pp. 275–292 in: Proc. 6th Int. Conf. on Harmonic Analysis and Partial Differential Equations (El Escorial, 2000), Publ. Mat.Google Scholar

[276] Villani, C. 2003. Topics in Optimal Transportation. Graduate Studies in Mathematics, vol. 58. Providence, RI: American Mathematical Society.

[277] Vol'berg, A. L. and Konyagin, S. V. 1987. On measures with the doubling condition. Izv. Akad. Nauk SSSR Ser. Mat., 51, 666–675. English translation: Math. USSR-Izv., 30, 629–638, 1988.Google Scholar

[278] von Renesse, M.-K. and Sturm, K.-Th. 2005. Transport inequalities, gradient estimates, entropy, and Ricci curvature. Comm. Pure Appl. Math., 58(7), 923–940.Google Scholar

[279] Vuorinen, M. 1988. Conformal Geometry and Quasiregular Mappings. Berlin: Springer-Verlag.

[280] Wallin, H. 1963a. Continuous functions and potential theory. Ark. Mat., 5, 55–84.Google Scholar

[281] Wallin, H. 1963b. Studies in potential theory. Inaugural dissertation. Acta Universitatis Upsaliensis, Abstracts of Uppsala Dissertations in Science, vol. 26. Almqvist & Wiksells Boktryckeri AB, Uppsala.

[282] Weaver, N. 2000. Lipschitz algebras and derivations. II. Exterior differentiation. J. Funct. Anal., 178(1), 64–112.Google Scholar

[283] Whitney, H. 1934. Analytic extensions of differentiable functions defined in closed sets. Trans. Amer. Math. Soc., 36(1), 63–89.Google Scholar

[284] Williams, M. 2012. Geometric and analytic quasiconformality in metric measure spaces. Proc. Amer. Math. Soc., 140(4), 1251–1266.Google Scholar

[285] Wojtaszczyk, P. 1991. Banach Spaces for Analysts. Cambridge: Cambridge University Press.

[286] Yosida, K. 1980. Functional Analysis. New York: Springer-Verlag.

[287] Ziemer, W. P. 1967. Extremal length and conformal capacity. Trans. Amer. Math. Soc., 126, 460–473.Google Scholar

[288] Ziemer, W. P. 1969. Extremal length and p-capacity. Michigan Math. J., 16, 43–51.Google Scholar

[289] Ziemer, W. P. 1970. Extremal length as a capacity. Michigan Math. J., 17, 117–128.Google Scholar

[290] Ziemer, W. P. 1989. Weakly Differentiable Functions. Graduate Texts in Mathematics, vol. 120. New York: Springer-Verlag.