Boundedness properties of the maximal operator in a nonsymmetric inverse Gaussian setting
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arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866929690725318656 |
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| author | Bruno, Tommaso Casarino, Valentina Ciatti, Paolo Sjögren, Peter |
| author_facet | Bruno, Tommaso Casarino, Valentina Ciatti, Paolo Sjögren, Peter |
| contents | We introduce a generalized inverse Gaussian setting and consider the maximal operator associated with the natural analogue of a nonsymmetric Ornstein--Uhlenbeck semigroup. We prove that it is bounded on $L^{p}$ when $p\in (1,\infty]$ and that it is of weak type $(1,1)$, with respect to the relevant measure. For small values of the time parameter $t$, the proof hinges on the "forbidden zones" method previously introduced in the Gaussian context. But for large times the proof requires new tools. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_17517 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Boundedness properties of the maximal operator in a nonsymmetric inverse Gaussian setting Bruno, Tommaso Casarino, Valentina Ciatti, Paolo Sjögren, Peter Functional Analysis Probability 42B25, 47D03 We introduce a generalized inverse Gaussian setting and consider the maximal operator associated with the natural analogue of a nonsymmetric Ornstein--Uhlenbeck semigroup. We prove that it is bounded on $L^{p}$ when $p\in (1,\infty]$ and that it is of weak type $(1,1)$, with respect to the relevant measure. For small values of the time parameter $t$, the proof hinges on the "forbidden zones" method previously introduced in the Gaussian context. But for large times the proof requires new tools. |
| title | Boundedness properties of the maximal operator in a nonsymmetric inverse Gaussian setting |
| topic | Functional Analysis Probability 42B25, 47D03 |
| url | https://arxiv.org/abs/2501.17517 |