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

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985840%3A_____%2F25%3A00618200" target="_blank" >RIV/67985840:_____/25:00618200 - isvavai.cz</a>
Alternative codes found
RIV/47813059:19610/25:A0000199
Result on the web
<a href="https://doi.org/10.1016/j.jfa.2025.110857" target="_blank" >https://doi.org/10.1016/j.jfa.2025.110857</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.jfa.2025.110857" target="_blank" >10.1016/j.jfa.2025.110857</a>

Result language
angličtina
Original language name
A Moebius invariant space of H-harmonic functions on the ball
Original language description
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.
Czech name
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Czech description
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Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10101 - Pure mathematics

Project
<a href="/en/project/GA25-18042S" target="_blank" >GA25-18042S: Reproducing kernels in complex analysis</a><br>
Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year
2025
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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