  We obtain sharp weighted estimates for solutions of the equation $\partial$ u
= f in a lineally convex domain of finite type. Precisely we obtain estimates
in the spaces L p ($\Omega$,$\delta$ $\gamma$), $\delta$ being the distance to
the boundary, with two different types of hypothesis on the form f : first, if
the data f belongs to L p $\Omega$,$\delta$ $\gamma$ $\Omega$ , $\gamma$ > --1,
we have a mixed gain on the index p and the exponent $\gamma$; secondly we
obtain a similar estimate when the data f satisfies an apropriate anisotropic L
p estimate with weight $\delta$ $\gamma$+1 $\Omega$. Moreover we extend those
results to $\gamma$ = --1 and obtain L p ($\partial$ $\Omega$) and
BMO($\partial$ $\Omega$) estimates. These results allow us to extend the L p
($\Omega$,$\delta$ $\gamma$)-regularity results for weighted Bergman projection
obtained in [CDM14b] for convex domains to more general weights.
