Work

A Moebius invariant space of H-harmonic functions on the ball

Year: 2025

Type: article

Abstract: It has been an open problem — at least since M. Stoll's book “Harmonic and subharmonic function theory on the hyperbolic ball” (Cambridge University Press, 2016) — whether there exists a Moebius invariant Hilbert space of hyperbolic-harmonic functions on the unit ball of the real n -space, i.e. of functions annihilated by the hyperbolic Laplacian on the ball. We give an answer by describing a Dirichlet-type space of hyperbolic-harmonic functions, as the analytic continuation (in the spirit of Rossi and Vergne) of the corresponding weighted Bergman spaces. Characterizations in terms of derivatives are given, and the associated semi-inner product is shown to be Moebius invariant. We also give a formula for the corresponding reproducing kernel.

Source: Journal of Functional Analysis

DOI: 10.1016/j.jfa.2025.110857

Authors: Petr Blaschke, Miroslav Engliš, El-Hassan Youssfi

Institutions: Silesian University in Opava, Czech Academy of Sciences, Institute of Mathematics, Aix-Marseille Université, Institut de Mathématiques de Marseille

Language: English

Topic: Holomorphic and Operator Theory

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,250

Funders: Rijksdienst voor Ondernemend Nederland, Grantová Agentura České Republiky, Akademie Věd České Republiky