Boas-type theorems for the Dunkl transform in the space $L^{1}_{k}(R^{d},w_{k}(x)dx)$

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2025年9月22日

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A. Mahfoud,
M. El Hamma

摘要

The purpose of the present work is to study the necessary and sufficient condition in terms of the Dunkl transform ${\mathcal {F}}_{k}(f)$ $F_{k} (f)$ on ${{\mathbb {R}}}^{d}$ $R^{d}$ , to ensure that f belong either to one of the generalized Lipschitz classes $D_{\alpha }^{m}$ $D_{α}^{m}$ and $d_{\alpha }^{m}$ $d_{α}^{m}$ for $\alpha >0$ $α > 0$ .

Boas-type theorems for the Dunkl transform in the space \(L^{1}_{k}(R^{d},w_{k}(x)dx)\)

摘要