L p Estimates of certain rough parametric Marcinkiewicz functions

Laith Hawawsheh, Ahmad Al-Salman*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)

Abstract

We prove Lp estimates of a class of parametric Marcinkiewicz integral operators when their kernels satisfy only the L1(Sn 1) integrability condition. The obtained Lp estimates resolve a problem left open in previous work. Our argument is based on duality technique and direct estimation of operators. As a consequence of our result, we deduce the Lp boundedness of a class of fractional Marcinkiewicz integral operators.

Original languageEnglish
Pages (from-to)867-879
Number of pages13
JournalFrontiers of Mathematics in China
Volume14
Issue number5
DOIs
Publication statusPublished - Oct 1 2019

Keywords

  • Marcinkiewicz integrals
  • Marcinkiewicz interpolation theorem
  • parametric Marcinkiewicz functions
  • rough kernels

ASJC Scopus subject areas

  • Mathematics (miscellaneous)

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