Singular Integrals Associated with Zygmund Dilations

Yongsheng Han; Ji Li; Chin Cheng Lin; Chaoqiang Tan

doi:10.1007/s12220-018-0081-8

Singular Integrals Associated with Zygmund Dilations

Yongsheng Han, Ji Li, Chin Cheng Lin, Chaoqiang Tan

Department of Mathematics

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

9 Scopus citations

Abstract

The main purpose of this paper is to study multi-parameter singular integral operators which commute with Zygmund dilations. Motivated by some explicit examples of singular integral operators studied in Ricci and Stein (Ann Inst Fourier (Grenoble) 42:637–670, 1992), Fefferman and Pipher (Am J Math 11:337–369, 1997), and Nagel and Wainger (Am J Math 99:761–785, 1977), we introduce a class of singular integral operators on R³ associated with Zygmund dilations by providing suitable version of regularity conditions and cancellation conditions on convolution kernels, and then show the boundedness for this class of operators on L^p, 1 < p< ∞.

Original language	English
Pages (from-to)	2410-2455
Number of pages	46
Journal	Journal of Geometric Analysis
Volume	29
Issue number	3
DOIs	https://doi.org/10.1007/s12220-018-0081-8
State	Published - 15 Jul 2019

Keywords

Multi-parameter singular integral operators
Zygmund dilations
Zygmund type cancellation

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10.1007/s12220-018-0081-8

Bmo Spaces Associated with a Family of General Sets(2/3)
Lin, C.-C. (PI)
1/08/18 → 31/07/19
Project: Research

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T1 - Singular Integrals Associated with Zygmund Dilations

AU - Han, Yongsheng

AU - Li, Ji

AU - Lin, Chin Cheng

AU - Tan, Chaoqiang

PY - 2019/7/15

Y1 - 2019/7/15

N2 - The main purpose of this paper is to study multi-parameter singular integral operators which commute with Zygmund dilations. Motivated by some explicit examples of singular integral operators studied in Ricci and Stein (Ann Inst Fourier (Grenoble) 42:637–670, 1992), Fefferman and Pipher (Am J Math 11:337–369, 1997), and Nagel and Wainger (Am J Math 99:761–785, 1977), we introduce a class of singular integral operators on R3 associated with Zygmund dilations by providing suitable version of regularity conditions and cancellation conditions on convolution kernels, and then show the boundedness for this class of operators on Lp, 1 < p< ∞.

AB - The main purpose of this paper is to study multi-parameter singular integral operators which commute with Zygmund dilations. Motivated by some explicit examples of singular integral operators studied in Ricci and Stein (Ann Inst Fourier (Grenoble) 42:637–670, 1992), Fefferman and Pipher (Am J Math 11:337–369, 1997), and Nagel and Wainger (Am J Math 99:761–785, 1977), we introduce a class of singular integral operators on R3 associated with Zygmund dilations by providing suitable version of regularity conditions and cancellation conditions on convolution kernels, and then show the boundedness for this class of operators on Lp, 1 < p< ∞.

KW - Multi-parameter singular integral operators

KW - Zygmund dilations

KW - Zygmund type cancellation

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DO - 10.1007/s12220-018-0081-8

M3 - 期刊論文

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SN - 1050-6926

VL - 29

SP - 2410

EP - 2455

JO - Journal of Geometric Analysis

JF - Journal of Geometric Analysis

IS - 3

ER -

Singular Integrals Associated with Zygmund Dilations

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Keywords

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