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Poisson representations of Dunkl harmonic functions satisfying a Carleson condition
Abstract
We prove that a smooth Dunkl harmonic function in the upper half-space whose Dunkl gradient satisfies a Carleson measure condition is the Poisson integral of a function in BMO(dw), defined using Euclidean balls. The result holds for arbitrary finite root systems and nonnegative multiplicities. The proof uses an estimate for increments from the origin, obtained from a finite-dimensional system indexed by the reflection group, together with the atomic characterization of the Dunkl Hardy space.
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BibTeX
@misc{dziubanski2026poisson,
title = {{Poisson representations of Dunkl harmonic functions satisfying a Carleson condition}},
author = {Jacek Dziubański and Rafał Łyżwa},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.10956},
eprint = {2610.10956},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.10956},
}
RIS
TY - UNPB
TI - Poisson representations of Dunkl harmonic functions satisfying a Carleson condition
AU - Jacek Dziubański
AU - Rafał Łyżwa
PY - 2026
DA - 2026/10/07
PB - arXiv
DO - 10.48550/arxiv.2610.10956
UR - https://arxiv.org/abs/2610.10956
AB - We prove that a smooth Dunkl harmonic function in the upper half-space whose Dunkl gradient satisfies a Carleson measure condition is the Poisson integral of a function in BMO(dw), defined using Euclidean balls. The result holds for arbitrary finite root systems and nonnegative multiplicities. The proof uses an estimate for increments from the origin, obtained from a finite-dimensional system indexed by the reflection group, together with the atomic characterization of the Dunkl Hardy space.
ER -