Decay of q-Dunkl transforms and generalized Lipschitz spaces

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发表日期：

2025年1月28日

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Othman Tyr

摘要

Based on the concept of generalized modulus of smoothness, we obtain sufficient conditions for the decay of q-Dunkl transforms associated with the q-Dunkl operator connected with q-Dunkl translation operators in the weighted space $L^{2}_{q,\nu }({\mathbb {R}}_{q})$ $L_{q, ν}^{2} (R_{q})$ . These conditions generalize well known Titchmarsh conditions for functions from Lipschitz classes. A characterization of Besov spaces in terms of the decay of q-Dunkl transform is also verified.