Weighted Lp boundedness of Marcinkiewicz integral

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Abstract

A weighted norm inequality for the Marcinkiewicz integral operator μΩ is proved when Ω belongs to H1(Sn-1), n ≥ 2. We also give the weighted Lp-boundedness for a class of Marcinkiewicz integral operators with rough kernels μ Ω,λ* and μΩ,S related to the Littlewood-Paley gλ*-function and the area integral S, respectively.

Original languageEnglish
Pages (from-to)211-220
Number of pages10
JournalIntegral Equations and Operator Theory
Volume49
Issue number2
DOIs
StatePublished - 2004

Keywords

  • Area integral
  • Hardy space
  • Marcinkiewicz integral
  • Rough kernel
  • g*-function
  • g-function

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