A Banach space that distinguishes two maximal operators
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| Accesso online: | |
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| _version_ | 1866913137372954624 |
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| author | Kovač, Vjekoslav |
| author_facet | Kovač, Vjekoslav |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_17663 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A Banach space that distinguishes two maximal operators Kovač, Vjekoslav Classical Analysis and ODEs Functional Analysis 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. |
| title | A Banach space that distinguishes two maximal operators |
| topic | Classical Analysis and ODEs Functional Analysis |
| url | https://arxiv.org/abs/2605.17663 |