IJPAM: Volume 119, No. 4 (2018)

Title

BOUNDEDNESS OF MAXIMAL FUNCTIONS
WITH MIXED HOMOGENEITY

Authors

Hiyam Al-Bataineh$^1$, Mohammed Ali$^2$
$^1$Department of Mathematics and Statistics
Jordan University of Science and Technology
P.O. Box 3030, Irbid, 22110, JORDAN
$^2$Department of Mathematics and Statistics
Jordan University of Science and Technology
P.O. Box 3030, Irbid, 22110, JORDAN

Abstract

In this article, we study a certain class of maximal functions with mixed homogeneity when the kernels in $L^q(\mathbf{S}^{n-1})$ for $1<q\leq2$. We obtain appropriate $L^p$ estimates for such maximal operators. These estimates will allow us to use extrapolation arguments to establish the $L^p$ boundedness of our maximal functions when their kernels belong to $ L(\log L)^{1/\gamma'}( \mathbf{S} ^{n-1})\cup B^{(0,-1/\gamma)}_q( \mathbf{S}^{n-1})$ with $q>1$ and $1\leq \gamma \leq2$. Our results essentially improve and extend some known results on maximal functions as well as singular integrals.

History

Received: April 5, 2017
Revised: August 2, 2018
Published: August 10, 2018

AMS Classification, Key Words

AMS Subject Classification: 40B20, 40B15, 40B25
Key Words and Phrases: $L^p$ boundedness, maximal operators, rough kernels

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Bibliography

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How to Cite?

DOI: 10.12732/ijpam.v119i4.12 How to cite this paper?

Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2018
Volume: 119
Issue: 4
Pages: 705 - 716


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