$\overline{\partial}$-Estimates on the product of bounded Lipschitz domain
Fuente:
arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| Acceso en línea: | |
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| _version_ | 1866914931870269440 |
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| author | Li, Song-Ying Long, Sujuan Lao, Jie |
| author_facet | Li, Song-Ying Long, Sujuan Lao, Jie |
| contents | Let $D$ be a bounded domain in the complex plane with Lipschitz boundary. In the paper, we construct an integral solution operator $T[f]$ for any $\overline{\partial}$ closed $(0,1)$-form $f\in L^p_{(0,1)}(D^n)$ solving the Cauchy-Riemain equation $\overline{\partial} u=f$ on the product domains $D^n$ and obtain the $L^p$-estimates for all $1<p\le \infty$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_00293 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | $\overline{\partial}$-Estimates on the product of bounded Lipschitz domain Li, Song-Ying Long, Sujuan Lao, Jie Complex Variables 32W05 Let $D$ be a bounded domain in the complex plane with Lipschitz boundary. In the paper, we construct an integral solution operator $T[f]$ for any $\overline{\partial}$ closed $(0,1)$-form $f\in L^p_{(0,1)}(D^n)$ solving the Cauchy-Riemain equation $\overline{\partial} u=f$ on the product domains $D^n$ and obtain the $L^p$-estimates for all $1<p\le \infty$. |
| title | $\overline{\partial}$-Estimates on the product of bounded Lipschitz domain |
| topic | Complex Variables 32W05 |
| url | https://arxiv.org/abs/2409.00293 |