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Acta Mathematica Vietnamica

On Weighted Lp-Sobolev Estimates for Solutions of the -equation on Linearly Convex Domains of Finite Type and Application

icon-email P. Charpentier , Y. Dupain

Abstract

We obtain some weighted Lp-Sobolev estimates with gain on p and the weight for solutions of the -equation in linearly convex domains of finite type in Cn and apply them to obtain weighted Lp-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.