Lp bounds for a class of Marcinkiewicz integral operators

Ahmad Al-Salman*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

In this paper, we introduce a class of mappings that is more general than the class of polynomials as well as the class of convex functions. We prove Lp estimates of Marcinkiewicz integral operators along surfaces generated by mappings belong to this class. Moreover, we establish the Lp boundedness of the corresponding maximal functions. Our results extend as well as improve previously known results on Marcinkiewicz integral operators and maximal functions.

Original languageEnglish
Pages (from-to)165-182
Number of pages18
JournalJournal of Integral Equations and Applications
Volume31
Issue number2
DOIs
Publication statusPublished - 2019
Externally publishedYes

Keywords

  • at curves
  • Area integral
  • Fourier transform
  • Littlewood-Paley g* functions
  • Marcinkiewicz integrals
  • Rough kernels

ASJC Scopus subject areas

  • Numerical Analysis
  • Applied Mathematics

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