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JOURNALS // Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika // Archive

Izv. Vyssh. Uchebn. Zaved. Mat., 2024 Number 9, Pages 3–15 (Mi ivm10010)

Integrability and Boas type results for a generalized Fourier–Bessel transform

S. S. Volosivets

Saratov State University, 83 Astrakhanskaya str., Saratov, 410012 Russia

Abstract: We obtain sufficient conditions for weighted integrability of a generalized Fourier–Bessel transform of functions from generalized integral Lipschitz classes. These conditions are analogues of the well known Moricz conditions for classical Fourier transform. Also a Boas type result connecting the behavior of a function and the smoothness of its generalized Fourier–Bessel transform is proved.

Keywords: generalized Fourier–Bessel transform, generalized Fourier–Bessel translation, weighted integrability, generalized contraction.

UDC: 517.518.362

Received: 13.10.2023
Revised: 13.10.2023
Accepted: 26.12.2023

DOI: 10.26907/0021-3446-2024-9-3-15



© Steklov Math. Inst. of RAS, 2025