$\bar\partial$ Sobolev-type inequality and an improved $L^2$-estimate of $\bar\partial$ on bounded strictly pseudoconvex domains
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| Format: | Preprint |
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2024
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| _version_ | 1866916659855360000 |
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| author | Deng, Fusheng Jiang, Weiwen Qin, Xiangsen |
| author_facet | Deng, Fusheng Jiang, Weiwen Qin, Xiangsen |
| contents | We prove several Sobolev-type inequalities related to the $\bar\partial$-operator on bounded domains in $\mathbb{C}^n$, which can be viewed as a $\bar\partial$-version of the classical Sobolev inequality and its various generalizations, and apply them to derive a generalization of the Sobolev Inequality with Trace in $\mathbb{R}^n$. As applications to complex analysis, we get an integral form of Maximum Modulus Principle for holomorphic functions, and an improvement of Hörmander's $L^2$-estimate for $\bar\partial$ on bounded strictly pseudoconvex domains. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_15597 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | $\bar\partial$ Sobolev-type inequality and an improved $L^2$-estimate of $\bar\partial$ on bounded strictly pseudoconvex domains Deng, Fusheng Jiang, Weiwen Qin, Xiangsen Complex Variables We prove several Sobolev-type inequalities related to the $\bar\partial$-operator on bounded domains in $\mathbb{C}^n$, which can be viewed as a $\bar\partial$-version of the classical Sobolev inequality and its various generalizations, and apply them to derive a generalization of the Sobolev Inequality with Trace in $\mathbb{R}^n$. As applications to complex analysis, we get an integral form of Maximum Modulus Principle for holomorphic functions, and an improvement of Hörmander's $L^2$-estimate for $\bar\partial$ on bounded strictly pseudoconvex domains. |
| title | $\bar\partial$ Sobolev-type inequality and an improved $L^2$-estimate of $\bar\partial$ on bounded strictly pseudoconvex domains |
| topic | Complex Variables |
| url | https://arxiv.org/abs/2401.15597 |