On the boundedness of Dunkl multipliers
Volume 281 / 2025
Studia Mathematica 281 (2025), 77-100
MSC: Primary 42B15; Secondary 42B25, 47G10, 47B34
DOI: 10.4064/sm240626-24-11
Published online: 3 February 2025
Abstract
We use Littlewood–Paley–Stein theory to prove two versions of Dunkl multiplier theorem when the multiplier $m$ satisfies a modified Hörmander condition. When $m$ is radial we give a simple proof of a known result. For general $m$ we prove that the Dunkl multiplier operator takes radial functions in $L^p $ boundedly into $L^p$ for all $p \geq 2$.
