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.

中文翻译：

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$$p$$-Adic 傅立叶变换的加权可积性

我们获得了定义在 $$p$$ -adic 线性空间上的函数的充分条件，提供了它们的傅立叶变换的加权可积性。与平滑度模量相关的 Bernstein-Szasz 型条件在某种意义上是尖锐的。作为推论，我们推导出 SS Platonov 的最新结果。我们还证明了 Zygmund 类型测试，用于具有有界 $$s$$ -fluctuation 并属于 Holder 类的函数的可积性。