Publications & Preprints 

Poisson representations of Dunkl harmonic functions satisfying a Carleson condition

Jacek Dziubański and Rafał Łyżwa

Preprint (2026) | arXiv:2610.10956 [math.FA]

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 the Dunkl BMO space. 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.

Dimension dependence and dimension-free $\ell^2$ estimates for variation seminorms of spherical means on the hypercube

Rafał Łyżwa

Preprint (2026) | arXiv:2605.18713 [math.FA]

We prove that the $\ell^2 \to \ell^2$ norm of the $r$-variation seminorm of spherical means on the hypercube admits no dimension-free bounds for any $r \in [1, \infty)$ when the variation is taken over all possible radii. Furthermore, we establish that if the radii are restricted to a fixed parity, dimension-free estimates hold for all $r \in (2, \infty)$.