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

J 2025

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

BLASCHKE, Petr; Miroslav ENGLIŠ a El-Hassan YOUSSFI

Základní údaje

Originální název

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

Autoři

BLASCHKE, Petr; Miroslav ENGLIŠ a El-Hassan YOUSSFI

Vydání

Journal of Functional Analysis, San Diego (USA), Academic Press Inc. Elsevier Science, 2025, 0022-1236

Další údaje

Jazyk

angličtina

Typ výsledku

Článek v odborném periodiku

Stát vydavatele

Spojené státy

Utajení

není předmětem státního či obchodního tajemství

Odkazy

Journal of Functional Analysis

Impakt faktor

Impact factor: 1.600 v roce 2024

Označené pro přenos do RIV

Organizační jednotka

Matematický ústav v Opavě

DOI

https://doi.org/10.1016/j.jfa.2025.110857

UT WoS

001428202100001

EID Scopus

2-s2.0-85217866674

Klíčová slova anglicky

Dirichlet space; H-harmonic function; Hyperbolic Laplacian; Reproducing kernel

Štítky

MÚ, RIV26

Příznaky

Mezinárodní význam, Recenzováno

Návaznosti

GA25-18042S, projekt VaV.

Změněno: 23. 2. 2026 14:30, Mgr. Aleš Ryšavý

Anotace

V originále

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.

Citovat

BLASCHKE, Petr; Miroslav ENGLIŠ a El-Hassan YOUSSFI. A Moebius invariant space of H-harmonic functions on the ball. Journal of Functional Analysis. San Diego (USA): Academic Press Inc. Elsevier Science, 2025, roč. 288, č. 9, s. "110857-1"-"110857-33", 33 s. ISSN 0022-1236. Dostupné z: https://doi.org/10.1016/j.jfa.2025.110857.

@article{90863,
   author = {Blaschke, Petr and Engliš, Miroslav and Youssfi, ElandHassan},
   article_location = {San Diego (USA)},
   article_number = {9},
   doi = {https://doi.org/10.1016/j.jfa.2025.110857},
   keywords = {Dirichlet space; H-harmonic function; Hyperbolic Laplacian; Reproducing kernel},
   language = {eng},
   issn = {0022-1236},
   journal = {Journal of Functional Analysis},
   title = {A Moebius invariant space of H-harmonic functions on the ball},
   url = {https://www.sciencedirect.com/science/article/pii/S0022123625000394},
   volume = {288},
   year = {2025}
}

TY  - JOUR
ID  - 90863
AU  - Blaschke, Petr - Engliš, Miroslav - Youssfi, El-Hassan
PY  - 2025
TI  - A Moebius invariant space of H-harmonic functions on the ball
JF  - Journal of Functional Analysis
VL  - 288
IS  - 9
SP  - "110857-1"-"110857-33"
EP  - "110857-1"-"110857-33"
PB  - Academic Press Inc. Elsevier Science
SN  - 00221236
KW  - Dirichlet space
KW  - H-harmonic function
KW  - Hyperbolic Laplacian
KW  - Reproducing kernel
UR  - https://www.sciencedirect.com/science/article/pii/S0022123625000394
N2  - 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.
ER  -

BLASCHKE, Petr; Miroslav ENGLIŠ a El-Hassan YOUSSFI. A Moebius invariant space of H-harmonic functions on the ball. \textit{Journal of Functional Analysis}. San Diego (USA): Academic Press Inc. Elsevier Science, 2025, roč.~288, č.~9, s.~''110857-1''-''110857-33'', 33 s. ISSN~0022-1236. Dostupné z: https://doi.org/10.1016/j.jfa.2025.110857.

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