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arXiv · 2410.07655

Sobolev and H\"older estimates for the $\overline \partial$ equation on pseudoconvex domains of finite type in $\mathbb C^2$

Ziming Shi
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Abstract

We prove a homotopy formula which yields almost sharp estimates in all (positive-indexed) Sobolev and H\"older-Zygmund spaces for the $\overline \partial$ equation on pseudoconvex domains of finite type in $\mathbb C^2$, extending the earlier results of Fefferman-Kohn (1988), Range (1990), and Chang-Nagel-Stein (1992). The main novelty of our proof is the construction of holomorphic support functions that admit precise estimates when the parameter variable lies in a thin shell outside the domain.

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Ziming Shi. 2024-10-10. Sobolev and H\"older estimates for the $\overline \partial$ equation on pseudoconvex domains of finite type in $\mathbb C^2$. https://arxiv.org/abs/2410.07655

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