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Abstract <p> Sufficient dyadic conditions are obtained for functions in the Lebesgue space <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(L^{p}([0, +\infty))\)</EquationSource> </InlineEquation> with <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(1\leq p\leq 2\)</EquationSource> </InlineEquation>, ensuring the integrability of their Fourier-Walsh transforms. These conditions are expressed in terms of moduli of smoothness and are shown to be sharp. As a result, a recent result established by Platonov in this framework is deduced. </p>

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Generalized Dyadic Conditions Ensuring the Integrability of Fourier-Walsh Transforms

  • 期刊论文

  • 发表日期：

    2026年5月6日

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  • Othman Tyr

摘要

Abstract

Sufficient dyadic conditions are obtained for functions in the Lebesgue space \(L^{p}([0, +\infty))\) with \(1\leq p\leq 2\) , ensuring the integrability of their Fourier-Walsh transforms. These conditions are expressed in terms of moduli of smoothness and are shown to be sharp. As a result, a recent result established by Platonov in this framework is deduced.