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arXiv · 2501.17517

Boundedness properties of the maximal operator in a nonsymmetric inverse Gaussian setting

Tommaso Bruno·Valentina Casarino·Paolo Ciatti·Peter Sjögren
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Abstract

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.

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Tommaso Bruno, Valentina Casarino, Paolo Ciatti, Peter Sjögren. 2025-01-29. Boundedness properties of the maximal operator in a nonsymmetric inverse Gaussian setting. https://arxiv.org/abs/2501.17517

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