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Research Article | Open Access

Hardy-type spaces and Hardy-type inequalities

Saifallah Ghobber1( ), Hatem Mejjaoli2
Department of Mathematics and Statistics, College of Science, King Faisal University, P.O. Box 400, Al-Ahsa 31982, Saudi Arabia
Department of Mathematics, College of Sciences, Taibah University, P.O. Box 30002, Al Madinah Al Munawarah 42353, Saudi Arabia
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Abstract

In the present paper, we defined and then studied Hardy spaces related to spherical mean operators. We proved Hardy-type inequalities, then we showed refined Sobolev-type inequalities between homogeneous Riesz-type spaces, homogeneous Besov-type spaces, and Lorentz-type spaces. Next, we introduced and studied Hausdorff operators on generalized Hardy spaces. Finally, we investigated maximal Bochner-Riesz operators on generalized Hardy spaces.

Keywords

Hardy-type inequalitiesHausdorff operatorsmaximal Bochner-Riesz operators
CLC number: 46F12, 42B35

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AIMS Mathematics
Volume 10 Issue 7,
July 2025
Pages 15264-15293
DOI: 10.3934/math.2025684

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Ghobber S, Mejjaoli H. Hardy-type spaces and Hardy-type inequalities. AIMS Mathematics, 2025, 10(7): 15264-15293. https://doi.org/10.3934/math.2025684

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Received: 27 April 2025
Revised: 20 June 2025
Accepted: 27 June 2025
Published: 15 July 2025
©2025 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)