Abstract

The paper deals with boundedness problem for maximal operators associated to hypersurfaces in the space of integrable functions with degree p. A necessary condition for boundedness is given in the space of square-integrable functions in the case one nonvanishing principal curvature. A criterion for the boundedness of the maximal operators in the space of square-integrable functions is obtained for a partial class of convex hypersurfaces.

中文翻译：

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关于最大算子的估计

摘要

本文讨论了与p次可积函数空间中的超曲面相关的最大算子的有界问题。在主曲率不为零的情况下，在平方可积函数空间中给出了有界性的必要条件。对于部分类凸超曲面，获得了平方可积函数空间中最大算子有界性的准则。