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<p>This work presents necessary and sufficient conditions for the weighted integrability of the linear canonical Dunkl transforms of functions belonging to generalized Lipschitz classes. These results generalize two theorems originally established by Titchmarsh and also extend them to broader cases. In the <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(L^{2}\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mi>L</mi> <mn>2</mn> </msup> </math></EquationSource> </InlineEquation>-case, we further establish the sharpness of these conditions.</p>

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TITCHMARSH-TYPE RESULTS AND INTEGRABILITY FOR THE LINEAR CANONICAL DUNKL TRANSFORMS

  • 期刊论文

  • 发表日期：

    2026年3月23日

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  • Othman Tyr

摘要

This work presents necessary and sufficient conditions for the weighted integrability of the linear canonical Dunkl transforms of functions belonging to generalized Lipschitz classes. These results generalize two theorems originally established by Titchmarsh and also extend them to broader cases. In the \(L^{2}\) L 2 -case, we further establish the sharpness of these conditions.