On Weighted $L^{p}$-Sobolev Estimates for Solutions of the $\overline{\partial}$-equation on Lineally Convex Domains of Finite Type and Application

P. Charpentier; Y. Dupain

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arXiv · 2312.03394

On Weighted $L^{p}$-Sobolev Estimates for Solutions of the $\overline{\partial}$-equation on Lineally Convex Domains of Finite Type and Application

P. Charpentier·Y. Dupain

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Abstract

We obtain some weighted $L^{p}$-Sobolev estimates with gain on $p$ and the weight for solutions of the $\overline{\partial}$-equation in lineally convex domains of finite type in $\mathbb{C}^{n}$ and apply them to obtain weighted $L^{p}$-Sobolev estimates for weighted Bergman projections of convex domains of finite type for quite general weights equivalent to a power of the distance to the boundary.

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P. Charpentier, Y. Dupain. 2023-12-06. On Weighted $L^{p}$-Sobolev Estimates for Solutions of the $\overline{\partial}$-equation on Lineally Convex Domains of Finite Type and Application. https://arxiv.org/abs/2312.03394

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