Two-weight inequality for the heat flow and solvability of Hardy-Hénon parabolic equation
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arXiv
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866916335962816512 |
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| author | Tsutsui, Yohei |
| author_facet | Tsutsui, Yohei |
| contents | In this article, we provide two-weight inequalities for the heat flow on the whole space by applying the sparse domination. For power weights, such inequalities were given by several authors. Owing to the sparse domination, we can treat general weights in Muckenhoupt classes. As a application, we present the local and global existence results for the Hardy-Hénon parabolic equation, which has a potential belonging to a Muckenhoupt class. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_17704 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Two-weight inequality for the heat flow and solvability of Hardy-Hénon parabolic equation Tsutsui, Yohei Classical Analysis and ODEs Analysis of PDEs 42B37, 35K15 In this article, we provide two-weight inequalities for the heat flow on the whole space by applying the sparse domination. For power weights, such inequalities were given by several authors. Owing to the sparse domination, we can treat general weights in Muckenhoupt classes. As a application, we present the local and global existence results for the Hardy-Hénon parabolic equation, which has a potential belonging to a Muckenhoupt class. |
| title | Two-weight inequality for the heat flow and solvability of Hardy-Hénon parabolic equation |
| topic | Classical Analysis and ODEs Analysis of PDEs 42B37, 35K15 |
| url | https://arxiv.org/abs/2407.17704 |