Supnorm estimates for $\bar\partial$ on product domains in $\mathbb{C}^n$

Martino Fassina; Yifei Pan

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arXiv · 1903.10475

Supnorm estimates for $\bar\partial$ on product domains in $\mathbb{C}^n$

Martino Fassina·Yifei Pan

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Abstract

Let $\Omega\subset\mathbb{C}^n$ be a product of one-dimensional open bounded domains with $C^{1,\alpha}$ boundary, where $0<\alpha<1$. Using methods from complex analysis in one variable, we construct an integral operator that solves $\bar\partial$ in $\Omega$ with supnorm estimates when the datum is in $C^{n-1,\alpha}(\Omega)$.

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Martino Fassina, Yifei Pan. 2019-03-25. Supnorm estimates for $\bar\partial$ on product domains in $\mathbb{C}^n$. https://arxiv.org/abs/1903.10475

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