Year: 2026
Type: preprint
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 $\mathrm{BMO}(dw)$, 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.
Source: arXiv (Cornell University)
Authors: Dziubański, Jacek, Łyżwa, Rafał
Institution: University of Wrocław
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7221072739