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

S. S. Volosivets

Izvestiâ vysših učebnyh zavedenij. Matematika, no. 9 (2024), pp. 3-15

Résumé

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.

Détail

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

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