Weighted estimates of the Bergman projection with matrix weights

Abstract

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.

19 pages. With some typos fixed. arXiv admin note: text overlap with arXiv:2001.07868

References in corpus (1)

• Bekollé-Bonami estimates on some pseudoconvex domains