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Weighted integrability of $$p$$-adic Fourier transform. (English) Zbl 1456.30081
Summary: We obtain sufficient conditions for functions defined on $$p$$-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 $$s$$-fluctuation and belonging to a Hölder class.
##### MSC:
 30G06 Non-Archimedean function theory 42A38 Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type
##### Keywords:
$$p$$-adic linear space; Fourier transform
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##### References:
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