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2016 A Class of Parabolic Maximal Functions
Ghada Shakkah, Ahmad Al-Salman
Commun. Math. Anal. 19(2): 1-31 (2016).

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 $L\log L^{\frac{1}{2}}(\mathbb{S}^{n-1})$ or in the block space $B_{q}^{0,-1/2}(\mathbb{S}^{n-1}),$ $q>1$.

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Ghada Shakkah. Ahmad Al-Salman. "A Class of Parabolic Maximal Functions." Commun. Math. Anal. 19 (2) 1 - 31, 2016.

Information

Published: 2016
First available in Project Euclid: 17 February 2016

zbMATH: 1333.42039
MathSciNet: MR3451687

Subjects:
Primary: 42B20

Keywords: Block space , maximal functions , Oscillatory integrals , Parabolic maximal functions , singular integrals

Rights: Copyright © 2016 Mathematical Research Publishers

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Vol.19 • No. 2 • 2016
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