{"ID":22938770,"CreatedAt":"2026-09-17T01:37:05.451791504Z","UpdatedAt":"2026-09-17T01:37:05.451791504Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2609.18621","arxiv_id":"2609.18621","title":"A Remark on Hörmander Multipliers on Dunkl Hardy Spaces","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 $H^p_{\\mathrm{Dunkl}}$, $0\u003cp\\le1$, defined by conical Littlewood--Paley square functions. Let $W_2^s$ denote the classical Sobolev space in $\\mathbb{R}^N$. More precisely, if a multiplier $m$ satisfies \\[ \\sup_{t\u003e0} \\|ψ(\\cdot)m(t\\cdot)\\|_{W_2^s}\u003c\\infty \\] for a nonzero radial cutoff $ψ\\in C_c^\\infty(\\mathbb R^N\\setminus\\{0\\})$ and \\[ s\u003e\\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 $H^p_{\\mathrm{Dunkl}}$.","short_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 $H^p_{\\mathrm{Dunkl}}$, $0\u003cp\\le1$, defined by conical Littlewood--Paley square functions. Let $W...","url_abs":"https://arxiv.org/abs/2609.18621","url_pdf":"https://arxiv.org/pdf/2609.18621v1","authors":"[\"Jacek Dziubański\",\"Agnieszka Hejna-Łyżwa\"]","published":"2026-09-16T13:10:39Z","proceeding":"math.FA","tasks":"[\"math.FA\"]","methods":"[]","has_code":false}