On a class of singular integral operators with rough kernels

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14 Citations (Scopus)

Abstract

In this paper, we study the Lp mapping properties of a class of singular integral operators with rough kernels belonging to certain block spaces. We prove that our operators are bounded on Lp provided that their kernels satisfy a size condition much weaker than that for the classical Calderón-Zygmund singular integral operators. Moreover, we present an example showing that our size condition is optimal. As a consequence of our results, we substantially improve a previously known result on certain maximal functions.

Original languageEnglish
Pages (from-to)3-10
Number of pages8
JournalCanadian Mathematical Bulletin
Volume49
Issue number1
Publication statusPublished - Mar 2006

Keywords

  • Block spaces
  • Maximal functions
  • Rough kernels
  • Singular integrals
  • Square functions

ASJC Scopus subject areas

  • Mathematics(all)

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