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On Weighted $L^{p}$-Sobolev Estimates for Solutions of the $\overline{\partial }$-equation on Linearly Convex Domains of Finite Type and Application
P. Charpentier
,
Y. Dupain
Abstract
We obtain some weighted $L^{p}$-Sobolev estimates with gain on p and the weight for solutions of the $\overline{\partial }$-equation in linearly 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.