Abstract

The paper deals with maximal operators associated with a family of singular hypersurfaces in the space \(\mathbb{R}^{n+1}\). The boundedness of these operators in the space of integrable functions is proved for the case in which the singular hypersurfaces are given by parametric equations. The boundedness exponent of maximal operators for spaces of integrable functions is found.

中文翻译：

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奇异超曲面的极大算子有界性

摘要

该论文讨论了与空间\(\mathbb{R}^{n+1}\)中一系列奇异超曲面相关的最大算子。对于奇异超曲面由参数方程给出的情况，证明了这些算子在可积函数空间中的有界性。找到可积函数空间的最大算子的有界指数。