The purpose of this work is to prove an analog of the classical Titchmarsh’s theorem (Introduction to the theory of Fourier integrals, Oxford University Press, Oxford, 1937, Theorem 84) and Younis’s Theorem (Fourier transform of Lipschitz functions on compact groups, Ph.D. Thesis, McMaster University, Hamilton, Ontario, Canada, 1974, Theorem 2.6) on the image under the discrete Fourier–Jacobi transform of a set of functions satisfying a generalized Lipschitz condition in the weighted spaces \({\mathbb {L}}_{p}([0,\pi ]) \), \(1<p\le 2\). For this purpose, we use a generalized translation operator which was defined by Flensted-Jensen and Koornwinder in (The convolution structure for Jacobi function expansions, Ark. Mat., 1973)

这项工作的目的是证明经典的Titchmarsh定理（傅里叶积分理论简介，牛津大学出版社，牛津，1937年，定理84）和Younis定理（紧凑型群上Lipschitz函数的傅立叶变换）。 D.论文，麦克马斯特大学，加拿大安大略省汉密尔顿市，1974年，定理2.6）在离散傅立叶-雅各比变换下的图像在加权空间\（{\ mathbb {L} } _ {p}（[0，\ pi]）\），\（1 <p \ le 2 \）。为此，我们使用由Flensted-Jensen和Koornwinder在（Jacobi函数展开的卷积结构，Ark。Mat。，1973）中定义的广义转换算子。