2025
A Moebius invariant space of H-harmonic functions on the ball
BLASCHKE, Petr; Miroslav ENGLIŠ and El-Hassan YOUSSFIBasic information
Original name
A Moebius invariant space of H-harmonic functions on the ball
Authors
BLASCHKE, Petr; Miroslav ENGLIŠ and El-Hassan YOUSSFI
Edition
Journal of Functional Analysis, San Diego (USA), Academic Press Inc. Elsevier Science, 2025, 0022-1236
Other information
Language
English
Type of outcome
Article in a journal
Country of publisher
United States of America
Confidentiality degree
is not subject to a state or trade secret
References:
Impact factor
Impact factor: 1.600 in 2024
Marked to be transferred to RIV
No
Organization unit
Mathematical Institute in Opava
UT WoS
001428202100001
EID Scopus
2-s2.0-85217866674
Keywords in English
Dirichlet space; H-harmonic function; Hyperbolic Laplacian; Reproducing kernel
Tags
International impact, Reviewed
Links
GA25-18042S, research and development project.
Changed: 23/2/2026 14:30, Mgr. Aleš Ryšavý
Abstract
In the original language
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 nspace, i.e. of functions annihilated by the hyperbolic Laplacian on the ball. We give an answer by describing a Dirichlettype 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.