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arXiv · 2605.17663

A Banach space that distinguishes two maximal operators

Vjekoslav Kovač
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Abstract

Maz'ya and Shaposhnikova introduced a non-classical maximal operator $M^\diamond$ as the maximal convolution with the vector-valued signum kernel truncated to centered balls. We construct a translation-invariant Banach space of locally integrable functions on which $M^\diamond$ is bounded, but the sharp maximal operator $M^\sharp$ is not. This answers one of Maz'ya's questions from a collection of 75 open problems in analysis.

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Vjekoslav Kovač. 2026-05-17. A Banach space that distinguishes two maximal operators. https://arxiv.org/abs/2605.17663

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