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

^*Corresponding author for this work

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12 Citations (Scopus)

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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
Early online date	23 Aug 2018
DOIs	https://doi.org/10.1007/s12220-018-0081-8
Publication status	Published - Jul 2019

Bibliographical note

Copyright the Author(s) 2018. Version archived for private and non-commercial use with the permission of the author/s and according to publisher conditions. For further rights please contact the publisher.

Keywords

Multi-parameter singular integral operators
Zygmund dilations
Zygmund type cancellation

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10.1007/s12220-018-0081-8Licence: CC BY

Publisher version (open access)Final published version, 742 KBLicence: CC BY

Cite this

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AU - Li, Ji

AU - Lin, Chin-Cheng

AU - Tan, Chaoqiang

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KW - Zygmund type cancellation

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Singular integrals associated with Zygmund dilations

Abstract

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Keywords

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