Sharp quantitative integral inequalities for harmonic extensions
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866915444719353856 |
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| author | Frank, Rupert L. Peteranderl, Jonas W. Read, Larry |
| author_facet | Frank, Rupert L. Peteranderl, Jonas W. Read, Larry |
| contents | We prove a quantitative version of a sharp integral inequality by Hang, Wang, and Yan for both the Poisson operator and its adjoint. Our result has the strongest possible norm and the optimal stability exponent. This stability exponent is not necessarily equal to 2, displaying the same phenomenon that Figalli and Zhang observed for the $p$-Sobolev inequality. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_09940 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Sharp quantitative integral inequalities for harmonic extensions Frank, Rupert L. Peteranderl, Jonas W. Read, Larry Analysis of PDEs Classical Analysis and ODEs Functional Analysis We prove a quantitative version of a sharp integral inequality by Hang, Wang, and Yan for both the Poisson operator and its adjoint. Our result has the strongest possible norm and the optimal stability exponent. This stability exponent is not necessarily equal to 2, displaying the same phenomenon that Figalli and Zhang observed for the $p$-Sobolev inequality. |
| title | Sharp quantitative integral inequalities for harmonic extensions |
| topic | Analysis of PDEs Classical Analysis and ODEs Functional Analysis |
| url | https://arxiv.org/abs/2508.09940 |