Fractional Maximal operator in hyperbolic spaces
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866911743288016896 |
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| author | Ibañez-Firnkorn, Gonzalo Ramadori, Emanuel |
| author_facet | Ibañez-Firnkorn, Gonzalo Ramadori, Emanuel |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2312_17410 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Fractional Maximal operator in hyperbolic spaces Ibañez-Firnkorn, Gonzalo Ramadori, Emanuel Classical Analysis and ODEs 43A85 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. |
| title | Fractional Maximal operator in hyperbolic spaces |
| topic | Classical Analysis and ODEs 43A85 |
| url | https://arxiv.org/abs/2312.17410 |