A class of parabolic maximal functions

Ghada Shakkah; Ahmad Al-Salman

A class of parabolic maximal functions

Ghada Shakkah, Ahmad Al-Salman

Mathematics & Statistics

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

4 Citations (Scopus)

Abstract

In this paper, we prove L^p estimates of a class of parabolic maximal functions provided that their kernels are in L^q . Using the obtained estimates, we prove the boundedness of the maximal functions under very weak conditions on the kernel. In particular, we prove the L^p -boundedness of our maximal functions when their kernels are in Llog L^1/2 (S^n-1 ) or in the block space Bq ^0,?1/2(S^n?1 ), q>1.

Original language	English
Pages (from-to)	1-31
Number of pages	31
Journal	Communications in Mathematical Analysis
Volume	19
Issue number	2
Publication status	Published - 2016

Keywords

Block space.
Maximal functions
Oscillatory integrals
Parabolic maximal functions
Singular integrals

ASJC Scopus subject areas

Analysis
Numerical Analysis
Computational Mathematics
Applied Mathematics

Cite this

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abstract = "In this paper, we prove Lp estimates of a class of parabolic maximal functions provided that their kernels are in Lq . Using the obtained estimates, we prove the boundedness of the maximal functions under very weak conditions on the kernel. In particular, we prove the Lp -boundedness of our maximal functions when their kernels are in Llog L1/2 (Sn-1 ) or in the block space Bq 0,?1/2(Sn?1 ), q>1.",

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author = "Ghada Shakkah and Ahmad Al-Salman",

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journal = "Communications in Mathematical Analysis",

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AU - Shakkah, Ghada

AU - Al-Salman, Ahmad

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AB - In this paper, we prove Lp estimates of a class of parabolic maximal functions provided that their kernels are in Lq . Using the obtained estimates, we prove the boundedness of the maximal functions under very weak conditions on the kernel. In particular, we prove the Lp -boundedness of our maximal functions when their kernels are in Llog L1/2 (Sn-1 ) or in the block space Bq 0,?1/2(Sn?1 ), q>1.

KW - Block space.

KW - Maximal functions

KW - Oscillatory integrals

KW - Parabolic maximal functions

KW - Singular integrals

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VL - 19

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JO - Communications in Mathematical Analysis

JF - Communications in Mathematical Analysis

IS - 2

ER -

A class of parabolic maximal functions

Abstract

Keywords

ASJC Scopus subject areas

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