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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2504.19273 |
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| _version_ | 1866917551460581376 |
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| author | He, Tianyang Liu, Zhiwen Yu, Ting |
| author_facet | He, Tianyang Liu, Zhiwen Yu, Ting |
| contents | In this paper, we first study the sharp weak estimate for the $p$-adic $n$-dimensional fractional Hardy operator from $L^p$ to $L^{q,\infty}$. Secondly, we study the sharp bounds for the $m$-linear $n$-dimensional $p$-adic integral operator with a kernel on $p$-adic weighted spaces $H_α^{\infty}( \mathbb{Q} _{p}^{n} )$. As an application, the sharp bounds for $p$-adic Hardy and Hilbert operators on $p$-adic weighted spaces are obtained. Finally, we also find the sharp bound for the Hausdorff operator on $p$-adic weighted spaces, which generalizes the previous results. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_19273 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Sharp bounds for the $\boldsymbol{p}$-adic $\boldsymbol{n}$-dimensional fractional Hardy operator and a class of integral operators on $\boldsymbol{p}$-adic function spaces He, Tianyang Liu, Zhiwen Yu, Ting Functional Analysis Primary 42B25, Secondary 42B20, 47H60, 47B47 In this paper, we first study the sharp weak estimate for the $p$-adic $n$-dimensional fractional Hardy operator from $L^p$ to $L^{q,\infty}$. Secondly, we study the sharp bounds for the $m$-linear $n$-dimensional $p$-adic integral operator with a kernel on $p$-adic weighted spaces $H_α^{\infty}( \mathbb{Q} _{p}^{n} )$. As an application, the sharp bounds for $p$-adic Hardy and Hilbert operators on $p$-adic weighted spaces are obtained. Finally, we also find the sharp bound for the Hausdorff operator on $p$-adic weighted spaces, which generalizes the previous results. |
| title | Sharp bounds for the $\boldsymbol{p}$-adic $\boldsymbol{n}$-dimensional fractional Hardy operator and a class of integral operators on $\boldsymbol{p}$-adic function spaces |
| topic | Functional Analysis Primary 42B25, Secondary 42B20, 47H60, 47B47 |
| url | https://arxiv.org/abs/2504.19273 |