Kragujevac Journal of Mathematics
University of Kragujevac - Faculty of Science

On the $q$-Bessel Transform of Lipschitz and Dini-Lipschitz Functions on Weighted Space $\mathcal{L}^{p}_{q,\nu}(\mathbb{R}_{q}^{ })$

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Authors: O. TYR AND R. DAHER

DOI: 10.46793/KgJMat2506.831T

Abstract:

E. C. Titchmarsh proved some theorems (Theorems 84 and 85) on the classical Fourier transform of functions satisfying conditions related to the Cauchy-Lipschitz conditions in the one-dimensional case. In this paper, we obtain a generalization of those theorems for the q-Bessel transform of a set of functions satisfying the q-Bessel-Lipschitz condition of certain order in suitable weighted spaces ℒ_q,ν^p(ℝ_q⁺), where 1 < p ≤ 2. In addition, we introduce the q-Bessel-Dini-Lipschitz condition and we obtain analogous of Titchmarsh’s theorems in this occurrence.

Keywords:

q-Bessel operator, q-Bessel transform, generalized q-Bessel translation, Lipschitz class, Dini-Lipschitz class, Titchmarsh’s theorems.

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