A class of marcinkiewicz type integral operators

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2 Citations (Scopus)

Abstract

We introduce a class of integral operators related to parametric Marcinkiewicz operators. We present a multiplier formula characterizing the L2 boundedness of such class of operators. Also, we prove L p (inhomogeneous Sobolev space)→Lp estimates provided that the kernels are in L(logL)(Sn-1). In fact, we show that the global parts of the introduced operators are bounded on the Lebesgue spaces Lp(1 < p < ∞) while the local parts are bounded on certain Sobolev spaces Lp.

Original languageEnglish
Pages (from-to)56-81
Number of pages26
JournalCommunications in Mathematical Analysis
Volume13
Issue number2
Publication statusPublished - 2012

Keywords

  • Bessel functions
  • Fourier transform
  • Marcinkiewicz integrals
  • Rough integral operators
  • Sobolev spaces
  • Triebel-Lizorkin space

ASJC Scopus subject areas

  • Analysis
  • Numerical Analysis
  • Computational Mathematics
  • Applied Mathematics

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