Quantitative Weighted Bounds for the q-Variation of Singular Integrals with Rough Kernels

Yanping Chen; Guixiang Hong; Ji Li

doi:10.1007/s00041-023-10006-6

Quantitative Weighted Bounds for the q-Variation of Singular Integrals with Rough Kernels

Yanping Chen^*
, Guixiang Hong
, Ji Li

^*Corresponding author for this work

School of Mathematics

University of Science and Technology Beijing
Macquarie University

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

5 Scopus citations

Abstract

In this paper, we study the quantitative weighted bounds for the q-variational singular integral operators with rough kernels, a stronger nonlinearity than the maximal truncations. The main result is for the truncated singular integrals itself ‖Vq{TΩ,ε}ε>0‖Lp(w)→Lp(w)≲‖Ω‖L∞(w)Ap1+1/q{w}Ap, it is the best known quantitative result for this class of operators. In the course of establishing the above estimate, we obtain several quantitative weighted bounds which are of independent interest.

Original language	English
Article number	31
Journal	Journal of Fourier Analysis and Applications
Volume	29
Issue number	3
DOIs	https://doi.org/10.1007/s00041-023-10006-6
State	Published - Jun 2023

Keywords

Quantitative weighted bounds
Rough kernel
Singular integral operator
Variation inequality

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10.1007/s00041-023-10006-6

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title = "Quantitative Weighted Bounds for the q-Variation of Singular Integrals with Rough Kernels",

abstract = "In this paper, we study the quantitative weighted bounds for the q-variational singular integral operators with rough kernels, a stronger nonlinearity than the maximal truncations. The main result is for the truncated singular integrals itself ‖Vq\{TΩ,ε\}ε>0‖Lp(w)→Lp(w)≲‖Ω‖L∞(w)Ap1+1/q\{w\}Ap, it is the best known quantitative result for this class of operators. In the course of establishing the above estimate, we obtain several quantitative weighted bounds which are of independent interest.",

keywords = "Quantitative weighted bounds, Rough kernel, Singular integral operator, Variation inequality",

author = "Yanping Chen and Guixiang Hong and Ji Li",

note = "Publisher Copyright: {\textcopyright} 2023, The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature.",

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T1 - Quantitative Weighted Bounds for the q-Variation of Singular Integrals with Rough Kernels

AU - Chen, Yanping

AU - Hong, Guixiang

AU - Li, Ji

PY - 2023/6

Y1 - 2023/6

N2 - In this paper, we study the quantitative weighted bounds for the q-variational singular integral operators with rough kernels, a stronger nonlinearity than the maximal truncations. The main result is for the truncated singular integrals itself ‖Vq{TΩ,ε}ε>0‖Lp(w)→Lp(w)≲‖Ω‖L∞(w)Ap1+1/q{w}Ap, it is the best known quantitative result for this class of operators. In the course of establishing the above estimate, we obtain several quantitative weighted bounds which are of independent interest.

AB - In this paper, we study the quantitative weighted bounds for the q-variational singular integral operators with rough kernels, a stronger nonlinearity than the maximal truncations. The main result is for the truncated singular integrals itself ‖Vq{TΩ,ε}ε>0‖Lp(w)→Lp(w)≲‖Ω‖L∞(w)Ap1+1/q{w}Ap, it is the best known quantitative result for this class of operators. In the course of establishing the above estimate, we obtain several quantitative weighted bounds which are of independent interest.

KW - Quantitative weighted bounds

KW - Rough kernel

KW - Singular integral operator

KW - Variation inequality

UR - https://www.scopus.com/pages/publications/85160638205

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DO - 10.1007/s00041-023-10006-6

M3 - 文章

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SN - 1069-5869

VL - 29

JO - Journal of Fourier Analysis and Applications

JF - Journal of Fourier Analysis and Applications

IS - 3

M1 - 31

ER -

Quantitative Weighted Bounds for the q-Variation of Singular Integrals with Rough Kernels

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Keywords

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