Harmonic Berezin transform on half-space with vertical weights
Complex Variables
2023-12-15 v4 Functional Analysis
Abstract
We consider weighted harmonic Bergman spaces on upper half-space with weights depending only on the vertical coordinate. In these settings, we give full asymptotic expansion of weighted harmonic Bergman kernel as well as full asymptotic expansion of the harmonic Berezin transform for functions depending only on the vertical coordinate. Both expansions utilize known holomorphic case for the Siegel domain.
Cite
@article{arxiv.2310.17562,
title = {Harmonic Berezin transform on half-space with vertical weights},
author = {Jaroslav Bradík},
journal= {arXiv preprint arXiv:2310.17562},
year = {2023}
}