Riesz-Fejér inequalities for hyperbolic harmonic functions in the unit ball

Ali Ahmed; Adel Khalfallah

doi:10.1016/j.jmaa.2026.130826

Riesz-Fejér inequalities for hyperbolic harmonic functions in the unit ball

Ali Ahmed
, Adel Khalfallah^*

^*Corresponding author for this work

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

In this paper, we establish a Riesz–Fejér-type inequality for hyperbolic harmonic functions in the unit ball Bⁿ⊂Rⁿ. For functions in the hyperbolic harmonic Hardy space, we determine the optimal constant in an inequality relating the boundary L^p norm to a weighted radial integral. We also prove that the constant is sharp, extending recent results from the unit disk to higher dimensions.

Original language	English
Article number	130826
Journal	Journal of Mathematical Analysis and Applications
Volume	563
Issue number	2
DOIs	https://doi.org/10.1016/j.jmaa.2026.130826
State	Published - 15 Nov 2026

Bibliographical note

Publisher Copyright:
© 2026 Elsevier Inc.

Keywords

Harmonic functions
Hyperbolic Laplacian
Riesz–Fejér inequality
Schur test

ASJC Scopus subject areas

Analysis
Applied Mathematics

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10.1016/j.jmaa.2026.130826

Cite this

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title = "Riesz-Fej{\'e}r inequalities for hyperbolic harmonic functions in the unit ball",

abstract = "In this paper, we establish a Riesz{\textendash}Fej{\'e}r-type inequality for hyperbolic harmonic functions in the unit ball Bn⊂Rn. For functions in the hyperbolic harmonic Hardy space, we determine the optimal constant in an inequality relating the boundary Lp norm to a weighted radial integral. We also prove that the constant is sharp, extending recent results from the unit disk to higher dimensions.",

keywords = "Harmonic functions, Hyperbolic Laplacian, Riesz{\textendash}Fej{\'e}r inequality, Schur test",

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AU - Khalfallah, Adel

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N2 - In this paper, we establish a Riesz–Fejér-type inequality for hyperbolic harmonic functions in the unit ball Bn⊂Rn. For functions in the hyperbolic harmonic Hardy space, we determine the optimal constant in an inequality relating the boundary Lp norm to a weighted radial integral. We also prove that the constant is sharp, extending recent results from the unit disk to higher dimensions.

AB - In this paper, we establish a Riesz–Fejér-type inequality for hyperbolic harmonic functions in the unit ball Bn⊂Rn. For functions in the hyperbolic harmonic Hardy space, we determine the optimal constant in an inequality relating the boundary Lp norm to a weighted radial integral. We also prove that the constant is sharp, extending recent results from the unit disk to higher dimensions.

KW - Harmonic functions

KW - Hyperbolic Laplacian

KW - Riesz–Fejér inequality

KW - Schur test

UR - https://www.scopus.com/pages/publications/105040115930

U2 - 10.1016/j.jmaa.2026.130826

DO - 10.1016/j.jmaa.2026.130826

M3 - Article

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SN - 0022-247X

VL - 563

JO - Journal of Mathematical Analysis and Applications

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M1 - 130826

ER -

Riesz-Fejér inequalities for hyperbolic harmonic functions in the unit ball

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

Access to Document

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Cite this