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<p>In this paper, we establish Titchmarsh-type theorems for the canonical Bessel transform acting on Lipschitz functions in <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(\mathcal {L}_{p,\nu }\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi mathvariant="script">L</mi> <mrow> <mi>p</mi> <mo>,</mo> <mi>ν</mi> </mrow> </msub> </math></EquationSource> </InlineEquation>-spaces. We characterize the decay and integrability properties of the canonical Bessel transform under appropriate Lipschitz and Dini–Lipschitz-type conditions. As applications, we obtain quantitative Riemann–Lebesgue-type estimates and prove integrability results for the transform, extending classical one-dimensional arguments of Titchmarsh to the framework of canonical Bessel analysis.</p>

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AN ANALOGUE OF TITCHMARSH’S THEOREM FOR THE CANONICAL BESSEL TRANSFORM IN WEIGHTED \(\mathcal {L}_{p,\nu }(\mathbb {R}_+)\) SPACES

  • 期刊论文

  • 发表日期：

    2026年5月21日

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  • Salah El Ouadih,
  • Ahmed Jmaiai

摘要

In this paper, we establish Titchmarsh-type theorems for the canonical Bessel transform acting on Lipschitz functions in \(\mathcal {L}_{p,\nu }\) L p , ν -spaces. We characterize the decay and integrability properties of the canonical Bessel transform under appropriate Lipschitz and Dini–Lipschitz-type conditions. As applications, we obtain quantitative Riemann–Lebesgue-type estimates and prove integrability results for the transform, extending classical one-dimensional arguments of Titchmarsh to the framework of canonical Bessel analysis.