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引用次数: 0
摘要
本文给出了在Damek-Ricci空间\(1<p\le 2\)上\(L^{p}\) -空间上定义的函数的充分条件，给出了它们的Fourier-Helgason变换的加权可积性。这些结果推广了著名的Titchmarsh定理和Younis定理，由于El Ouadih和Daher在Damek-Ricci空间上（El Ouadih和Daher in L C R Math Acad Sci Paris 359:675-685, 2021）。
Sufficient conditions for the weighted integrability of Fourier–Helgason transforms in the \(L^{p}\)-space on Damek–Ricci spaces
In this paper, we give sufficient conditions for functions defined on the \(L^{p}\)-space on Damek–Ricci spaces, \(1<p\le 2\), 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).
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