Communications in Mathematical Analysis

A Class of Parabolic Maximal Functions

Ghada Shakkah and Ahmad Al-Salman

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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 $B_{q}^{0,-1/2}(\mathbb{S}^{n-1}),$ $q>1$.

Article information

Source
Commun. Math. Anal., Volume 19, Number 2 (2016), 1-31.

Dates
First available in Project Euclid: 17 February 2016

Permanent link to this document
https://projecteuclid.org/euclid.cma/1455715866

Mathematical Reviews number (MathSciNet)
MR3451687

Zentralblatt MATH identifier
1333.42039

Subjects
Primary: 42B20: Singular and oscillatory integrals (Calderón-Zygmund, etc.)

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

Citation

Shakkah, Ghada; Al-Salman, Ahmad. A Class of Parabolic Maximal Functions. Commun. Math. Anal. 19 (2016), no. 2, 1--31. https://projecteuclid.org/euclid.cma/1455715866


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