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arXiv · 2312.17410

Fractional Maximal operator in hyperbolic spaces

Gonzalo Ibañez-Firnkorn·Emanuel Ramadori
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Abstract

In this article, we introduce the fractional maximal operator on the Hyperbolic space, a non-doubling measure space, and study the weighted boundedness. Motivated in the weighted boundedness of Hardy-Littlewood maximal studied by Antezana and Ombrosi in [1], we give conditions for the weak type and strong type estimate for fractional maximal. Also, we provide examples of weights for which the fractional maximal operator satisface weak type $(p,q)$ inequality but strong type $(p,q)$ inequality fails.

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BibTeXRIS

Gonzalo Ibañez-Firnkorn, Emanuel Ramadori. 2023-12-29. Fractional Maximal operator in hyperbolic spaces. https://arxiv.org/abs/2312.17410

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