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arXiv · 2610.10956

Poisson representations of Dunkl harmonic functions satisfying a Carleson condition

Jacek Dziubański·Rafał Łyżwa
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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.

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Jacek Dziubański, Rafał Łyżwa. 2026-10-07. Poisson representations of Dunkl harmonic functions satisfying a Carleson condition. https://arxiv.org/abs/2610.10956

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