Maximal polynomial modulations of singular Radon transforms

被引：0

作者：

Becker, Lars ^{[1
]}

机构：

[1] Univ Bonn, Math Inst, Endenicher Allee 60, D-53115 Bonn, Germany

来源：

JOURNAL OF FUNCTIONAL ANALYSIS | 2024年 / 286卷 / 06期

关键词：

Carleson operator; Radon Transform; Anisotropic dilations; Singular integrals; CONVERGENCE;

D O I：

10.1016/j.jfa.2023.110299

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We prove L2 -> Lp estimates on the torus for maximal polynomial modulations of Calderon-Zygmund operators with anisotropic scaling. We obtain improved constants in these estimates. As a corollary, maximal polynomial modulations of a mollified version of the Hilbert transform along the parabola are bounded with only logarithmic dependence of the estimate on the Lipschitz constant of the mollifier. (c) 2023 Elsevier Inc. All rights reserved.

引用

页数：46

共 50 条

[1] Maximal polynomial modulations of singular integrals
Zorin-Kranich, Pavel
[J]. ADVANCES IN MATHEMATICS, 2021, 386
[2] Singular and maximal Radon transforms: Analysis and geometry
Christ, M
Nagel, A
Stein, EM
Wainger, S
[J]. ANNALS OF MATHEMATICS, 1999, 150 (02) : 489 - 577
[3] Singular maximal functions and radon transforms near L
Seeger, A
Tao, T
Wright, J
[J]. AMERICAN JOURNAL OF MATHEMATICS, 2004, 126 (03) : 607 - 647
[4] Singular Radon transforms and maximal functions under convexity assumptions
Seeger, A
Wainger, S
[J]. REVISTA MATEMATICA IBEROAMERICANA, 2003, 19 (03) : 1019 - 1044
[5] SINGULAR RADON TRANSFORMS AND OSCILLATORY INTEGRALS
PHONG, DH
STEIN, EM
[J]. DUKE MATHEMATICAL JOURNAL, 1989, 58 (02) : 347 - 369
[6] DISCRETE ANALOGS OF SINGULAR RADON TRANSFORMS
STEIN, EM
WAINGER, S
[J]. BULLETIN OF THE AMERICAN MATHEMATICAL SOCIETY, 1990, 23 (02) : 537 - 544
[7] SOBOLEV ESTIMATES FOR SINGULAR RADON TRANSFORMS
THOMPSON, AA
[J]. JOURNAL OF FUNCTIONAL ANALYSIS, 1993, 112 (01) : 61 - 96
[8] SINGULAR VALUE DECOMPOSITIONS FOR RADON TRANSFORMS
MAASS, P
[J]. LECTURE NOTES IN MATHEMATICS, 1991, 1497 : 6 - 14
[9] Smooth and singular maximal averages over 2D hypersurfaces and associated Radon transforms
Greenblatt, Michael
[J]. ADVANCES IN MATHEMATICS, 2021, 377
[10] MULTI-PARAMETER SINGULAR RADON TRANSFORMS
Stein, Elias M.
Street, Brian
[J]. MATHEMATICAL RESEARCH LETTERS, 2011, 18 (02) : 257 - 277

← 1 2 3 4 5 →