Singular integrals associated with Zygmund dilations

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

Research output: Contribution to journalArticleResearchpeer-review

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 Lp, 1 < p< ∞.

LanguageEnglish
Pages2410-2455
Number of pages46
JournalJournal of Geometric Analysis
Volume29
Issue number3
Early online date23 Aug 2018
DOIs
Publication statusPublished - Jul 2019

Fingerprint

Singular Integral Operator
Singular Integrals
Dilation
Commute
Regularity Conditions
Cancellation
Boundedness
Convolution
kernel
Operator
Class

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

Cite this

Han, Yongsheng ; Li, Ji ; Lin, Chin-Cheng ; Tan, Chaoqiang. / Singular integrals associated with Zygmund dilations. In: Journal of Geometric Analysis. 2019 ; Vol. 29, No. 3. pp. 2410-2455.
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Singular integrals associated with Zygmund dilations. / Han, Yongsheng; Li, Ji; Lin, Chin-Cheng; Tan, Chaoqiang.

In: Journal of Geometric Analysis, Vol. 29, No. 3, 07.2019, p. 2410-2455.

Research output: Contribution to journalArticleResearchpeer-review

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