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

Q2 Mathematics

Annali dell''Universita di Ferrara Pub Date : 2025-09-22 DOI:10.1007/s11565-025-00612-1

A. Mahfoud, M. El Hamma

引用次数: 0

Abstract

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

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空间中Dunkl变换的boas型定理 \(L^{1}_{k}(R^{d},w_{k}(x)dx)\)

本文的目的是研究\({{\mathbb {R}}}^{d}\)上的Dunkl变换\({\mathcal {F}}_{k}(f)\)的充要条件，以保证f属于\(\alpha >0\)的广义Lipschitz类\(D_{\alpha }^{m}\)和\(d_{\alpha }^{m}\)之一。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Annali dell''Universita di Ferrara Mathematics-Mathematics (all)

CiteScore

1.70

自引率

0.00%

发文量

期刊介绍： Annali dell''Università di Ferrara is a general mathematical journal publishing high quality papers in all aspects of pure and applied mathematics. After a quick preliminary examination, potentially acceptable contributions will be judged by appropriate international referees. Original research papers are preferred, but well-written surveys on important subjects are also welcome.