Weak-type estimates for the Bergman projection on the polydisc and the Hartogs triangle

In this paper, we investigate the weak-type regularity of the Bergman projection. The two domains we focus on are the polydisc and the Hartogs triangle. For the polydisc, we provide a proof that the weak-type behavior is of ‘ (Formula presented.) ’ type. This result is likely known to the experts, but does not appear to be in the literature. For the Hartogs triangle, we show that the operator is of weak-type (4,4); settling the question of the behavior of the projection at this endpoint. At the other endpoint of interest, we show that the Bergman projection is not of weak-type (Formula presented.) and provide evidence as to what the correct behavior at this endpoint might be.