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The Poincaré Inequality and Reverse Doubling Weights

Published online by Cambridge University Press:  20 November 2018

Ritva Hurri-Syrjänen
Ritva Hurri-Syrjänen*
Affiliation:
Department of Mathematics P.O. Box 4 (Yliopiston katu 5) FIN-00014 University of Helsinki Finland, e-mail: hurrisyr@cc.helsinki.fi
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Abstract

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We show that Poincaré inequalities with reverse doubling weights hold in a large class of irregular domains whenever the weights satisfy certain conditions. Examples of these domains are John domains.

Keywords

46E35reverse doubling weightsPoincaré inequalityJohn domains
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 47 , Issue 2 , 01 June 2004 , pp. 206 - 214
Copyright
Copyright © Canadian Mathematical Society 2004

References

[1] Bojarski, B., Remarks on Sobolev imbedding inequalities. Complex Analysis, Joensuu 1987, Lecture Notes in Math. 1351, Springer, Berlin, 1988, 52–68.Google Scholar
[2] Hurri-Syrjänen, R., Unbounded Poincaré domains. Ann. Acad. Sci. Fenn. Ser. A I Math. 17 (1992), 409–423.Google Scholar
[3] Jones, P. W., Quasiconformal mappings and extendability of functions in Sobolev spaces. Acta Math. 147 (1981), 71–88.Google Scholar
[4] Martio, O., John domains, bilipschitz balls and Poincaré inequality. Rev. RoumaineMath. Pures Appl. 33 (1988), 107–112.Google Scholar
[5] Martio, O. and Sarvas, J., Injectivity theorems in plane and space. Ann. Acad. Sci. Fenn. Ser. A I Math. 4(1978–1979), 383–401.Google Scholar
[6] Näkki, R. and Väisälä, J., John disks. Exposition. Math. 9 (1991), 3–43.Google Scholar
[7] Sawyer, E. and Wheeden, R., Weighted inequalities for fractional integrals on euclidean and homogeneous spaces. Amer. J. Math. 114 (1992), 813–874.Google Scholar
[8] Stein, E. M., Singular Integrals and Differentiability Properties of Functions, Princeton University Press, Princeton, NJ, 1970.Google Scholar
[9] Väisälä, J., Quasiconformal maps of cylindrical domains. Acta Math. 162 (1989), 201–225.Google Scholar
[10] Väisälä, J., Exhaustions of John domains. Ann. Acad. Sci. Fenn. Ser. A I Math. 19 (1994), 47–57.Google Scholar