Sharp weak bounds for the Hardy-Littlewood-Pólya operator and the weak bounds for the multilinear integral operator
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866911737121341440 |
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| author | He, Tianyang |
| author_facet | He, Tianyang |
| contents | In this paper, we first obtain the operator norms of the $n$-dimensional Hardy-Littlewood-Pólya operator $\mathcal{H}$ from weighted Lebesgue spaces $L^p( \mathbb{R} ^n,| x |^β ) $ to weighted weak Lebesgue spaces $L^{q,\infty}(\mathbb{R} ^n,|x|^γ)$. Next, we obtain the weak bounds for the $m$-linear $n$-dimensional integral operator. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_17707 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Sharp weak bounds for the Hardy-Littlewood-Pólya operator and the weak bounds for the multilinear integral operator He, Tianyang Classical Analysis and ODEs Functional Analysis In this paper, we first obtain the operator norms of the $n$-dimensional Hardy-Littlewood-Pólya operator $\mathcal{H}$ from weighted Lebesgue spaces $L^p( \mathbb{R} ^n,| x |^β ) $ to weighted weak Lebesgue spaces $L^{q,\infty}(\mathbb{R} ^n,|x|^γ)$. Next, we obtain the weak bounds for the $m$-linear $n$-dimensional integral operator. |
| title | Sharp weak bounds for the Hardy-Littlewood-Pólya operator and the weak bounds for the multilinear integral operator |
| topic | Classical Analysis and ODEs Functional Analysis |
| url | https://arxiv.org/abs/2505.17707 |