Weighted estimates of the Bergman projection with matrix weights

We establish a weighted inequality for the Bergman projection with matrix weights for a class of pseudoconvex domains. We extend a result of Aleman-Constantin and obtain the following estimate for the weighted norm of $P$: [|P|_{L^2(Omega,W)}leq C(mathcal B_2(W))^{{2}}.] Here $mathcal B_2(W)$ is the Bekolle-Bonami constant for the matrix weight $W$ and $C$ is a constant that is independent of the weight $W$ but depends upon the dimension and the domain.