Maximal operators with rough kernels on product domains

Ahmad Al-Salman*

*Corresponding author for this work

Research output: Contribution to journalArticle

12 Citations (Scopus)

Abstract

In this paper, we study the Lp boundedness of certain maximal operators on product domains with rough kernels in L(log L). We prove that our operators are bounded on Lp for all 2 ≤ p < ∞. Moreover, we show that our condition on the kernel is optimal in the sense that the space L(log L) cannot be replaced by L(log)r for any r < 1. Our results resolve a problem left open in [Y. Ding, A note on a class of rough maximal operators on product domains, J. Math. Anal. Appl. 232 (1999) 222-228].

Original languageEnglish
Pages (from-to)338-351
Number of pages14
JournalJournal of Mathematical Analysis and Applications
Volume311
Issue number1
DOIs
Publication statusPublished - Nov 1 2005

Keywords

  • Maximal operators
  • Product domains
  • Rough kernels
  • Singular integrals

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

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