Weighted estimates for solutions of the $\partial$ -equation for lineally convex domains of finite type and applications to weighted bergman projections

In this paper we obtain sharp weighted estimates for solutions of the $\partial$-equation in a lineally convex domains of finite type. Precisely we obtain estimates in spaces of the form L p (Ω,$δ$ $γ$), $δ$ being the distance to the boundary, with gain on the index p and the exponent $γ$. These estimates allow us to extend the L p (Ω,$δ$ $γ$) and lipschitz regularity results for weighted Bergman projection obtained in [CDM14b] for convex domains to more general weights.

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