On the L2 boundedness of parametric Marcinkiewicz integral operator

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Abstract

In this paper, we derive a multiplier formula for Hörmander's parametric Marcinkiewicz integral operator. As a consequence, we prove the optimality of the kernel size condition L(logL)1/2(Sn-1) as well as the optimality of the Block size condition.

Original languageEnglish
Pages (from-to)745-752
Number of pages8
JournalJournal of Mathematical Analysis and Applications
Volume375
Issue number2
DOIs
Publication statusPublished - Mar 15 2011

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Keywords

  • Block spaces
  • Marcinkiewicz integrals
  • Parametric Marcinkiewicz integrals
  • Singular integrals

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

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