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Research Article | Open Access

Estimates for functions of generalized Marcinkiewicz operators related to surfaces of revolution

Mohammed Ali1, Qutaibeh Katatbeh1, Oqlah Al-Refai2( ), Basma Al-Shutnawi3
Department of Mathematics and Statistics, Faculty of Science and Arts, Jordan University of Science and Technology, P.O. Box 3030, Irbid 22110, Jordan
Department of Mathematics, Faculty of Science, Zarqa University, P.O.Box 132222, Zarqa 13132, Jordan
Department of mathematics, Faculty of Science, Tafila Technical University, P.O. Box 179, Tafila 66110, Jordan
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Abstract

In this paper, specific Lp estimates for generalized Marcinkiewicz operators correlated to surfaces of revolution are proved. These estimates and the extrapolation procedure of Yano are employed to confirm the Lp boundedness of the above-mentioned integrals under weaker assumptions on the singular kernels. Our findings generalize and improve several known results.

Keywords

Triebel-Lizorkin spacesingular kernelsgeneralized Marcinkiewicz integralsLp estimatesextrapolation
CLC number: 42B20, 42B25

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AIMS Mathematics
Volume 9 Issue 8,
August 2024
Pages 22287-22300
DOI: 10.3934/math.20241085

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Cite this article:
Ali M, Katatbeh Q, Al-Refai O, et al. Estimates for functions of generalized Marcinkiewicz operators related to surfaces of revolution. AIMS Mathematics, 2024, 9(8): 22287-22300. https://doi.org/10.3934/math.20241085

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Received: 09 May 2024
Revised: 03 July 2024
Accepted: 10 July 2024
Published: 15 August 2024
©2024 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0)