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<p>In this paper, using some elements of the q-harmonic analysis associated to the q-Dunkl operator introduced in [<CitationRef CitationID="CR3">3</CitationRef>], for fixed <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(0&lt;q&lt;1\)</EquationSource> </InlineEquation>, some new estimates useful in applications are proved for the generalized q-Dunkl transform in the space <InlineEquation ID="IEq4"> <EquationSource Format="TEX">\(L^{2}_{q,\alpha }(\mathbb {R}_{q})\)</EquationSource> </InlineEquation> as applied to some classes of functions characterized by a generalized modulus of continuity.</p>

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On estimates for the q-analogue of Dunkl transform in the weighted space \(L^{2}_{q,\alpha }(\mathbb {R}_{q})\)

  • 期刊论文

  • 发表日期：

    2026年2月28日

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  • Radouan Daher,
  • Othman Tyr

摘要

In this paper, using some elements of the q-harmonic analysis associated to the q-Dunkl operator introduced in [3], for fixed \(0<q<1\) , some new estimates useful in applications are proved for the generalized q-Dunkl transform in the space \(L^{2}_{q,\alpha }(\mathbb {R}_{q})\) as applied to some classes of functions characterized by a generalized modulus of continuity.