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arXiv · 1909.04080

Sup-norm Estimates for $\overline{\partial}$ in $\mathbb{C}^3$

Dusty Grundmeier·Lars Simon·Berit Stensønes
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Abstract

We develop a method for proving sup-norm and H\"older estimates for $\overline{\partial}$ on wide class of finite type pseudoconvex domains in $\mathbb{C}^n$. A fundamental obstruction to proving sup-norm estimates is the possibility of singular complex curves with exceptionally high order of contact with the boundary. Our method handles this problem, and in $\mathbb{C}^3$, we prove sup-norm and H\"older estimates for all bounded, pseudoconvex domains with real-analytic boundary.

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Dusty Grundmeier, Lars Simon, Berit Stensønes. 2019-09-09. Sup-norm Estimates for $\overline{\partial}$ in $\mathbb{C}^3$. https://arxiv.org/abs/1909.04080

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