The M-harmonic Dirichlet space on the ball

We describe the Dirichlet space of M -harmonic functions, i.e. functions annihilated by the invariant Laplacian on the unit ball of the complex n -space, as the limit of the analytic continuation (in the spirit of Rossi and Vergne) of the corresponding weighted Bergman spaces. Characterizations in terms of tangential derivatives are given, and the associated inner product is shown to be Moebius invariant. The pluriharmonic and harmonic cases are also briefly treated.

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Publication Details

Journal
Journal of Mathematical Analysis and Applications
Published
2024-12-13
DOI
https://doi.org/10.1016/j.jmaa.2024.129165
Primary Topic
Advanced Harmonic Analysis Research
Type
article
Field-Weighted Citation Impact
0.00

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article

The M-harmonic Dirichlet space on the ball

Miroslav Engliš, El Hassan Youssfi
Journal of Mathematical Analysis and Applications
Advanced Harmonic Analysis Research
article

The M-harmonic Dirichlet space on the ball

Miroslav Engliš, El Hassan Youssfi
article en

Abstract

We describe the Dirichlet space of M -harmonic functions, i.e. functions annihilated by the invariant Laplacian on the unit ball of the complex n -space, as the limit of the analytic continuation (in the spirit of Rossi and Vergne) of the corresponding weighted Bergman spaces. Characterizations in terms of tangential derivatives are given, and the associated inner product is shown to be Moebius invariant. The pluriharmonic and harmonic cases are also briefly treated.

Journal of Mathematical Analysis and ApplicationsVol. 545(2)
Centre National de la Recherche Scientifique (FR), Aix-Marseille Université (FR), Silesian University in Opava (CZ), Czech Academy of Sciences, Institute of Mathematics (CZ), Institut Polytechnique de Bordeaux (FR)
Rijksdienst voor Ondernemend Nederland, Grantová Agentura České Republiky, Akademie Věd České Republiky
Sustainable cities and communities
Openalex Percentile: Top 62%
Advanced Harmonic Analysis Research
DOIOpen Access PDFOpenAlex
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The M-harmonic Dirichlet space on the ball — Miroslav Engliš, El Hassan Youssfi · Journal of Mathematical Analysis and Applications (2024) | TGRS Research Map | TGRS