ABSTRACT

The purpose of this work is to prove analogues of the classical Titchmarsh theorem and Younis' theorem associated with the Fourier–Jacobi transform of a set of functions satisfying a generalized Lipschitz condition of a certain order in suitable weighted spaces $L^p\left(\right[0,+\mathrm{\infty }\left)\right)$, $1<p\le 2$. For this purpose, we use a generalized translation operator defined by Flensted-Jensen and Koornwinder.

中文翻译：

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满足 Lipschitz 和 Dini-Lipschitz 型估计的函数的 Fourier-Jacobi 变换的可积性

摘要

这项工作的目的是证明经典 Titchmarsh 定理和尤尼斯定理的类似物，这些定理与在合适的加权空间中满足特定阶的广义 Lipschitz 条件的一组函数的傅里叶-雅可比变换相关联 ${\mathrm{大号}}^p\left(\right[0,+\mathrm{\infty }\left)\right)$, $1<p\le 2$. 为此，我们使用由 Flensted-Jensen 和 Koornwinder 定义的广义翻译算子。