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arXiv · 2307.04951

Solving the Kerzman's problem on the sup-norm estimate for $\bar\partial$ on product domains

Song-Ying Li
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Abstract

In this paper, the author solves the long term open problem of Kerzman on sup-norm estimate for Cauchy-Riemann equation on polydisc in $n$-dimensional complex space. The problem has been open since 1971. He also extends and solves the problem on a bounded product domain $Ω^n$, where $Ω$ is any bounded domain in $\mathbb{C}$ with $C^{1,α}$ boundary for some $α>0$.

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Song-Ying Li. 2023-07-11. Solving the Kerzman's problem on the sup-norm estimate for $\bar\partial$ on product domains. https://arxiv.org/abs/2307.04951

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