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Sparse Bounds for a Prototypical Singular Radon Transform

Part of: Harmonic analysis in several variables

Published online by Cambridge University Press:  04 January 2019

Richard Oberlin
Richard Oberlin*
Affiliation:
Department of Mathematics, Florida State University, Tallahassee, FL 32306, USA Email: roberlin@math.fsu.edu
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Abstract

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We use a variant of a technique used by M. T. Lacey to give sparse $L^{p}(\log (L))^{4}$ bounds for a class of model singular and maximal Radon transforms.

Keywords

sparse dominationsingular radon transformmaximal radon transform

MSC classification

Primary: 42B25: Maximal functions, Littlewood-Paley theory
Type
Article
Information
Canadian Mathematical Bulletin , Volume 62 , Issue 2 , June 2019 , pp. 405 - 415
Copyright
© Canadian Mathematical Society 2018 

Footnotes

This material is based upon work supported by the National Science Foundation under Grant No. DMS-1440140 while the author was in residence at the Mathematical Sciences Research Institute in Berkeley, California, during the Spring 2017 semester.

References

Benea, C., Bernicot, F., and Luque, T., Sparse bilinear forms for Bochner Riesz multipliers and applications . Trans. London Math. Soc. 4(2017), no. 1, 110–128. https://doi.org/10.1112/tlm3.12005.Google Scholar
Bernicot, F., Frey, D., and Petermichl, S., Sharp weighted norm estimates beyond Calderón-Zygmund theory . Anal. PDE 9(2016), no. 5, 1079–1113. https://doi.org/10.2140/apde.2016.9.1079.Google Scholar
Cladek, L. and Krause, B., Improved endpoint bounds for the lacunary spherical maximal operator. 2017. arxiv:1703.01508.Google Scholar
Cladek, L. and Ou, Y., Sparse domination of Hilbert transforms along curves. 2017. arxiv:1704.07810.Google Scholar
Culiuc, A., Di Plinio, F., and Ou, Y., Domination of multilinear singular integrals by positive sparse forms. 2016. arxiv:1603.05317.Google Scholar
Culiuc, A., Kesler, R., and Lacey, M. T., Sparse bounds for the discrete cubic Hilbert transform. 2016. arxiv:1612.08881.Google Scholar
Di Plinio, F., Do, Y. Q., and Uraltsev, G.N., Positive sparse domination of variational Carleson operators. 2016. arxiv:1612.03028.Google Scholar
Duoandikoetxea, J. and Rubio de Francia, J. L., Maximal and singular integral operators via Fourier transform estimates . Invent. Math. 84(1986), no. 3, 541–561. https://doi.org/10.1007/BF01388746.Google Scholar
Krause, B. and Lacey, M. T., Sparse bounds for maximally truncated oscillatory singular integrals. 2017. arxiv:1701.05249.Google Scholar
Lacey, M. T., Sparse bounds for spherical maximal functions. 2017. arxiv:1702.08594.Google Scholar
Lacey, M. T., An elementary proof of the A 2 bound . Israel J. Math. 217(2017), 181–195. https://doi.org/10.1007/s11856-017-1442-x.Google Scholar
Lerner, A. K., A pointwise estimate for the local sharp maximal function with applications to singular integrals . Bull. Lond. Math. Soc. 42(2010), no. 5, 843–856. https://doi.org/10.1112/blms/bdq042.Google Scholar
Lerner, A. K., On pointwise estimates involving sparse operators . New York J. Math. 22(2016), 341–349.Google Scholar
Lerner, A. K. and Nazarov, F., Intuitive dyadic calculus: the basics. 2015. arxiv:1508.05639.Google Scholar
Nazarov, F., Petermichl, S., Treil, S., and Volberg, A., Convex body domination and weighted estimates with matrix weights . Adv. Math. 318(2017), 279–306. https://doi.org/10.1016/j.aim.2017.08.001.Google Scholar
Seeger, A., Tao, T., and Wright, J., Singular maximal functions and Radon transforms near L 1 . Amer. J. Math. 126(2004), no. 3, 607–647.Google Scholar