Geodesic
Sparse Bounds for a Prototypical Singular Radon Transform
Canadian mathematical bulletin, Tome 62 (2019) no. 2, pp. 405-415

Voir la notice de l'article provenant de la source Cambridge University Press

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.
DOI : 10.4153/CMB-2018-007-5
Mots-clés : sparse domination, singular radon transform, maximal radon transform 
Oberlin, Richard. Sparse Bounds for a Prototypical Singular Radon Transform. Canadian mathematical bulletin, Tome 62 (2019) no. 2, pp. 405-415. doi: 10.4153/CMB-2018-007-5
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[BBL16] 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. . Google Scholar | DOI

[BFP16] Bernicot, F., Frey, D., and Petermichl, S., Sharp weighted norm estimates beyond Calderón-Zygmund theory . Anal. PDE 9(2016), no. 5, 1079–1113. . Google Scholar | DOI

[CK17] Cladek, L. and Krause, B., Improved endpoint bounds for the lacunary spherical maximal operator. 2017. arxiv:1703.01508. Google Scholar

[CO] Cladek, L. and Ou, Y., Sparse domination of Hilbert transforms along curves. 2017. arxiv:1704.07810. Google Scholar

[CDO16] Culiuc, A., Di Plinio, F., and Ou, Y., Domination of multilinear singular integrals by positive sparse forms. 2016. arxiv:1603.05317. Google Scholar

[CKL16] Culiuc, A., Kesler, R., and Lacey, M. T., Sparse bounds for the discrete cubic Hilbert transform. 2016. arxiv:1612.08881. Google Scholar

[DDU16] Di Plinio, F., Do, Y. Q., and Uraltsev, G.N., Positive sparse domination of variational Carleson operators. 2016. arxiv:1612.03028. Google Scholar

[DRdF86] 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. . Google Scholar | DOI

[KL17] Krause, B. and Lacey, M. T., Sparse bounds for maximally truncated oscillatory singular integrals. 2017. arxiv:1701.05249. Google Scholar

[Lac17a] Lacey, M. T., Sparse bounds for spherical maximal functions. 2017. arxiv:1702.08594. Google Scholar

[Lac17b] Lacey, M. T., An elementary proof of the A bound . Israel J. Math. 217(2017), 181–195. . Google Scholar | DOI

[Ler10] 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. . Google Scholar | DOI

[Ler16] Lerner, A. K., On pointwise estimates involving sparse operators . New York J. Math. 22(2016), 341–349. Google Scholar

[LN15] Lerner, A. K. and Nazarov, F., Intuitive dyadic calculus: the basics. 2015. arxiv:1508.05639. Google Scholar

[NPTV17] Nazarov, F., Petermichl, S., Treil, S., and Volberg, A., Convex body domination and weighted estimates with matrix weights . Adv. Math. 318(2017), 279–306. . Google Scholar | DOI

[STW04] 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

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