Maximal polynomial modulations of singular Radon transforms

Lars Becker

doi:10.1016/j.jfa.2023.110299

Maximal polynomial modulations of singular Radon transforms

Lars Becker

Research output: Contribution to journal › Article › peer-review

2 Scopus citations

Abstract

We prove L²→L^p estimates on the torus for maximal polynomial modulations of Calderón-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.

Original language	English (US)
Article number	110299
Journal	Journal of Functional Analysis
Volume	286
Issue number	6
DOIs	https://doi.org/10.1016/j.jfa.2023.110299
State	Published - Mar 15 2024
Externally published	Yes

All Science Journal Classification (ASJC) codes

Analysis

Keywords

Anisotropic dilations
Carleson operator
Radon Transform
Singular integrals

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10.1016/j.jfa.2023.110299

Cite this

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title = "Maximal polynomial modulations of singular Radon transforms",

abstract = "We prove L2→Lp estimates on the torus for maximal polynomial modulations of Calder{\'o}n-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.",

keywords = "Anisotropic dilations, Carleson operator, Radon Transform, Singular integrals",

author = "Lars Becker",

note = "Publisher Copyright: {\textcopyright} 2023 Elsevier Inc.",

year = "2024",

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doi = "10.1016/j.jfa.2023.110299",

language = "English (US)",

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AU - Becker, Lars

PY - 2024/3/15

Y1 - 2024/3/15

N2 - We prove L2→Lp estimates on the torus for maximal polynomial modulations of Calderón-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.

AB - We prove L2→Lp estimates on the torus for maximal polynomial modulations of Calderón-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.

KW - Anisotropic dilations

KW - Carleson operator

KW - Radon Transform

KW - Singular integrals

UR - https://www.scopus.com/pages/publications/85182014411

UR - https://www.scopus.com/pages/publications/85182014411#tab=citedBy

U2 - 10.1016/j.jfa.2023.110299

DO - 10.1016/j.jfa.2023.110299

M3 - Article

AN - SCOPUS:85182014411

SN - 0022-1236

VL - 286

JO - Journal of Functional Analysis

JF - Journal of Functional Analysis

IS - 6

M1 - 110299

ER -

Maximal polynomial modulations of singular Radon transforms

Abstract

All Science Journal Classification (ASJC) codes

Keywords

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