Maximal operators with rough kernels on product domains

Ahmad Al-Salman

doi:10.1016/j.jmaa.2005.02.048

Maximal operators with rough kernels on product domains

Ahmad Al-Salman^*

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

16 Citations (Scopus)

Abstract

In this paper, we study the L^p boundedness of certain maximal operators on product domains with rough kernels in L(log L). We prove that our operators are bounded on L^p 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 language	English
Pages (from-to)	338-351
Number of pages	14
Journal	Journal of Mathematical Analysis and Applications
Volume	311
Issue number	1
DOIs	https://doi.org/10.1016/j.jmaa.2005.02.048
Publication status	Published - Nov 1 2005
Externally published	Yes

Keywords

Maximal operators
Product domains
Rough kernels
Singular integrals

ASJC Scopus subject areas

Analysis
Applied Mathematics

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10.1016/j.jmaa.2005.02.048

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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].",

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AB - 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].

KW - Maximal operators

KW - Product domains

KW - Rough kernels

KW - Singular integrals

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JF - Journal of Mathematical Analysis and Applications

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Maximal operators with rough kernels on product domains

Abstract

Keywords

ASJC Scopus subject areas

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