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 ({\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. 
Philippe Charpentier (IMB), Y Dupain (IMB), M Mounkaila (Universit\'e   Abdou Moumouni)
math.CV