Abstract
In this paper, we study the weak-type regularity of the Bergman projection on monomial polyhedra, which is a wide class of bounded singular pseudoconvex Reinhardt domains defined as sublevel sets of holomorphic monomials. We prove that the weak-type estimate of the Bergman projection holds at the upper endpoint of Lp boundedness range, but fails at the lower endpoint. This result generalizes the works of Huo-Wick and Christopherson-Koenig on 2-dimensional Hartogs triangles to a much more general setting, as well as the work of Jing et al. on n-dimensional generalized Hartogs triangle. As a consequence, we also obtain the weak-type regularity on the well-known elementary Reinhardt domains, which has not been considered by others.
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