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<p>In this paper, we give sufficient conditions for functions defined on the <InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="44146_2025_178_Article_IEq1.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="20" /> </InlineMediaObject> <EquationSource Format="TEX">\(L^{p}\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mi>L</mi> <mi>p</mi> </msup> </math></EquationSource> </InlineEquation>-space on Damek–Ricci spaces, <InlineEquation ID="IEq4"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="44146_2025_178_Article_IEq4.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="72" /> </InlineMediaObject> <EquationSource Format="TEX">\(1&lt;p\le 2\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mn>1</mn> <mo>&lt;</mo> <mi>p</mi> <mo>≤</mo> <mn>2</mn> </mrow> </math></EquationSource> </InlineEquation>, providing the weighted integrability of their Fourier–Helgason transforms. These results generalize a famous Titchmarsh’s theorem and Younis’ theorem, due to El Ouadih and Daher on Damek–Ricci spaces (El Ouadih and Daher in L C R Math Acad Sci Paris 359:675–685, 2021).</p>

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Sufficient conditions for the weighted integrability of Fourier–Helgason transforms in the \(L^{p}\)-space on Damek–Ricci spaces

  • 期刊论文

  • 发表日期：

    2025年2月24日

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  • Salah El Ouadih

摘要

In this paper, we give sufficient conditions for functions defined on the \(L^{p}\) L p -space on Damek–Ricci spaces, \(1<p\le 2\) 1 < p ≤ 2 , providing the weighted integrability of their Fourier–Helgason transforms. These results generalize a famous Titchmarsh’s theorem and Younis’ theorem, due to El Ouadih and Daher on Damek–Ricci spaces (El Ouadih and Daher in L C R Math Acad Sci Paris 359:675–685, 2021).