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 $P$: $\|P\|_{L^2(Ω,W)}\leq C(\mathcal B_2(W))^{2}.$ Here $\mathcal B_2(W)$ is the Bekollé-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.

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