Integrability of the Fourier–Jacobi transform of functions satisfying Lipschitz and Dini–Lipschitz-type estimates. Issue 2 (1st February 2022)

• Record Type: Journal Article
• Authors: Daher, Radouan; Tyr, Othman
• Is Part Of: Integral transforms and special functions. Volume 33:Issue 2(2022)
• Page Start: 115
• Page End: 126
• Publication Date: 2022-02-01
• Subjects: Fourier–Jacobi operator -- Fourier–Jacobi transform -- generalized translation operator -- Lipschitz class -- Dini–Lipschitz class -- Titchmarsh's theorem; 33C45 -- 41A17; Integral transforms -- Periodicals; Transcendental functions -- Periodicals; Transformations (Mathematics) -- Periodicals; Calculus, Integral -- Periodicals; 515
• DOI: 10.1080/10652469.2021.1913414
• Languages: English
• ISSNs: 1065-2469

Abstract

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 ( [ 0, + ∞ ) ), 1 < p ≤ 2 . For this purpose, we use a generalized translation operator defined by Flensted-Jensen and Koornwinder.