Singular integrals associated with Zygmund dilations

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

*Corresponding author for this work

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    4 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 Lp, 1 < p< ∞.

    Original languageEnglish
    Pages (from-to)2410-2455
    Number of pages46
    JournalJournal of Geometric Analysis
    Volume29
    Issue number3
    Early online date23 Aug 2018
    DOIs
    Publication statusPublished - 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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