Weighted Integrability of -Adic Fourier Transform

We obtain sufficient conditions for functions defined on -adic linear space providing the weighted integrability of their Fourier transforms. The Bernstein-Szasz type conditions connected with moduli of smoothness are sharp in a certain sense. As a corollary we deduce recent results of S. S. Platono...

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Bibliographic Details
Published in:P-adic numbers, ultrametric analysis, and applications ultrametric analysis, and applications, 2020, Vol.12 (3), p.203-209
Main Authors: Golubov, Boris I., Volosivets, Sergey S.
Format: Article
Language:English
Subjects:
14/34
639/766/189
639/766/530
639/766/747
Algebra
Fourier transforms
Integral calculus
Mathematics
Mathematics and Statistics
Smoothness
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Summary:We obtain sufficient conditions for functions defined on -adic linear space providing the weighted integrability of their Fourier transforms. The Bernstein-Szasz type conditions connected with moduli of smoothness are sharp in a certain sense. As a corollary we deduce recent results of S. S. Platonov. Also we prove Zygmund type tests for integrability of functions having bounded -fluctuation and belonging to a Hölder class.
ISSN:2070-0466
2070-0474
DOI:10.1134/S2070046620030036