Weighted <i>L<sup>p</sup></i> boundedness of maximal operators with rough kernels

Hussain Al-Qassem; Mohammed Ali; Hussain Al-Qassem; Mohammed Ali

doi:10.3934/math.20241269

AIMS Mathematics

2024, Volume 9, Issue 9: 25966-25978. doi: 10.3934/math.20241269

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Research article

Weighted L^p boundedness of maximal operators with rough kernels

Hussain Al-Qassem ^{1
,
,},
Mohammed Ali ²

1.
Department of Mathematics and Statistics, Qatar University, Doha, Qatar
2.
Department of Mathematics and Statistics, Faculty of Science and Arts, Jordan University of Science and Technology, P.O. Box 3030, Irbid 22110, Jordan

Received: 20 July 2024 Revised: 22 August 2024 Accepted: 27 August 2024 Published: 06 September 2024
MSC : 42B20, 42B25

In this paper, we study the weighted spaces $ L^p(\omega, \mathbb{R}^d) $ boundedness of certain class of maximal operators when their kernels belong to the space $ L^{q}(\mathbb{S} ^{d-1}) $, $ q > 1 $. Our results in this paper are improvements and extensions of some previously known results.
- maximal functions,
- $ L^p $ boundedness,
- rough kernels,
- surfaces of revolution,
- extrapolation
Citation: Hussain Al-Qassem, Mohammed Ali. Weighted Lp boundedness of maximal operators with rough kernels[J]. AIMS Mathematics, 2024, 9(9): 25966-25978. doi: 10.3934/math.20241269

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Abstract

In this paper, we study the weighted spaces $ L^p(\omega, \mathbb{R}^d) $ boundedness of certain class of maximal operators when their kernels belong to the space $ L^{q}(\mathbb{S} ^{d-1}) $, $ q > 1 $. Our results in this paper are improvements and extensions of some previously known results.

References

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