Abstract
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 Holder class.
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