Hardy-type spaces and Hardy-type inequalities

Saifallah Ghobber; Hatem Mejjaoli; Saifallah Ghobber; Hatem Mejjaoli

doi:10.3934/math.2025684

AIMS Mathematics

2025, Volume 10, Issue 7: 15264-15293. doi: 10.3934/math.2025684

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Hardy-type spaces and Hardy-type inequalities

Saifallah Ghobber ^{1
,
,},
Hatem Mejjaoli ²

1.
Department of Mathematics and Statistics, College of Science, King Faisal University, P.O. Box 400, Al-Ahsa 31982, Saudi Arabia
2.
Department of Mathematics, College of Sciences, Taibah University, P.O. Box 30002, Al Madinah Al Munawarah 42353, Saudi Arabia

Received: 27 April 2025 Revised: 20 June 2025 Accepted: 27 June 2025 Published: 02 July 2025
MSC : 46F12, 42B35

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.
- Hardy-type inequalities,
- Hausdorff operators,
- maximal Bochner-Riesz operators
Citation: Saifallah Ghobber, Hatem Mejjaoli. Hardy-type spaces and Hardy-type inequalities[J]. AIMS Mathematics, 2025, 10(7): 15264-15293. doi: 10.3934/math.2025684

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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.

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