Marcinkiewicz functions along flat surfaces with hardy space kernels

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Abstract

In this paper, we study Marcinkiewicz integral operators along subvarieties determined by flat surfaces with kernels in the Hardy space H1(Sn-1). We establish the Lp boundedness of our operators under weak convexity assumptions on the surfaces. Moreover, we establish the Lp boundedness of the corresponding Marcinkiewicz integral operators that are related to area integral and Littlewood-Paley gz.ast;λ functions. Our results offer substantial improvements of previously known results.

Original languageEnglish
Pages (from-to)357-373
Number of pages17
JournalJournal of Integral Equations and Applications
Volume17
Issue number4
DOIs
Publication statusPublished - 2005

Keywords

  • Area integral
  • Flat curves
  • Fourier transform
  • Littlewood-Paley g* functions
  • Marcinkiewicz integrals
  • Rough kernels

ASJC Scopus subject areas

  • Numerical Analysis
  • Applied Mathematics

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