Three results in Dunkl analysis
Volume 118 / 2010
Colloquium Mathematicum 118 (2010), 299-312 MSC: Primary 33C52; Secondary 42B10, 43A32, 33C80, 22E30. DOI: 10.4064/cm118-1-16
We first establish a geometric Paley–Wiener theorem for the Dunkl transform in the crystallographic case. Next we obtain an optimal bound for the $L^p\to L^p$ norm of Dunkl translations in dimension 1. Finally, we describe more precisely the support of the distribution associated to Dunkl translations in higher dimension.