Maximal operators with rough kernels on product domains

Research output: Contribution to journalArticle

11 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

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Rough Kernel
Maximal Operator
L-space
Rough
Boundedness
Resolve
kernel
Operator
Class

Keywords

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

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

Cite this

Maximal operators with rough kernels on product domains. / Al-Salman, Ahmad.

In: Journal of Mathematical Analysis and Applications, Vol. 311, No. 1, 01.11.2005, p. 338-351.

Research output: Contribution to journalArticle

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