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arXiv · 2409.00293

$\overline{\partial}$-Estimates on the product of bounded Lipschitz domain

Song-Ying Li·Sujuan Long·Jie Lao
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Abstract

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 $1<p\le \infty$.

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Song-Ying Li, Sujuan Long, Jie Lao. 2024-08-30. $\overline{\partial}$-Estimates on the product of bounded Lipschitz domain. https://arxiv.org/abs/2409.00293

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