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

Abstract

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 "$L\log L$" 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 $(\frac{4}{3},\frac{4}{3})$ and provide evidence as to what the correct behavior at this endpoint might be.

arXiv comment15 pages

References in corpus (6)

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Cited by in corpus (3)

• Projections onto $L^p$-Bergman spaces of Reinhardt Domains
• $L^p$ regularity of the Bergman projection on the symmetrized polydisc
• (Ir-)regularity of canonical projection operators on some weakly pseudoconvex domains