Abstract Let $$G$$ be a locally compact bounded Vilenkin group, $$\Gamma$$ be the dual group of $$G$$ . Suppose that a function $$f(x)$$ belongs to the the Lebesgue class $$L^p(G)$$ , $$10$$ , $$\beta\in{\mathbb R}$$ , then for which values of $$r$$ we can guarantee that $$\widehat{f}\in L^r(\Gamma)$$ ? The result is an analogue of one classical theorem of E. Titchmarsh about the Fourier transform of functions from the Lipschitz classes on $${\mathbb R}$$ .

中文翻译：

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局部紧维连金群上 Dini-Lipschitz 函数的傅里叶变换

摘要 令 $$G$$ 为局部紧有界 Vilenkin 群，$$\Gamma$$ 为 $$G$$ 的对偶群。假设函数 $$f(x)$$ 属于 Lebesgue 类 $$L^p(G)$$ , $$10$$ , $$\beta\in{\mathbb R}$$ ，那么对于 $$r$$ 的哪些值我们可以保证 $$\widehat{f}\in L^r(\Gamma)$$ ? 结果是 E. Titchmarsh 关于 $${\mathbb R}$$ 上 Lipschitz 类函数的傅立叶变换的一个经典定理的模拟。