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Weak-type estimates for the Bergman projection on the polydisc and the Hartogs triangle. (English) Zbl 07276233
Summary: 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.
##### MSC:
 32A25 Integral representations; canonical kernels (Szegő, Bergman, etc.) 32A36 Bergman spaces of functions in several complex variables
##### Keywords:
Bergman projection
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