  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 ({\Omega},$\delta$ $\gamma$),
$\delta$ being the distance to the boundary, with gain on the index p and the
exponent $\gamma$. These estimates allow us to extend the L p
({\Omega},$\delta$ $\gamma$) and lipschitz regularity results for weighted
Bergman projection obtained in [CDM14b] for convex domains to more general
weights.
