Year: 2026
Type: preprint
Abstract: Let $\mathcal R$ be a normalized root system in $\mathbb R^N$ with a nonnegative multiplicity function $k$, and let $\mathcal F$ be the associated Dunkl transform. We prove a Hörmander multiplier theorem on the Hardy spaces $H^p_{\mathrm{Dunkl}}$, $00} \|ψ(\cdot)m(t\cdot)\|_{W_2^s}<\infty \] for a nonzero radial cutoff $ψ\in C_c^\infty(\mathbb R^N\setminus\{0\})$ and \[ s>\mathbf N\left(\frac1p-\frac12\right), \] where $\mathbf N$ is the homogeneous dimension, then the Dunkl multiplier \[ \mathcal T_mf=\mathcal F^{-1}(m\mathcal Ff) \] extends to a bounded operator on $H^p_{\mathrm{Dunkl}}$.
Source: arXiv (Cornell University)
Authors: Dziubański, Jacek, Hejna-Łyżwa, Agnieszka
Institution: University of Wrocław
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7213527999