In this paper we introduce variable exponent Lebesgue spaces where the underlying space is the field of the p-adic numbers. We prove many properties of the spaces and also study the boundedness of the maximal operator as well as its application to convolution operators.

中文翻译：

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p-Adic 数上的可变指数 Lebesgue 空间和 Hardy-Littlewood 极大函数

在本文中，我们引入了可变指数 Lebesgue 空间，其中底层空间是 p-adic 数的域。我们证明了空间的许多性质，还研究了极大算子的有界性及其在卷积算子中的应用。