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

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