-norm Estimates of the Bergman Projection on the Monomial Polyhedra

作     者：Qin, Chuan Wang, Maofa Zhang, Shuo 

作者机构：Department of Mathematics School of Electronics and Information Engineering Taizhou University Taizhou China School of Mathematics and Statistics Wuhan University Wuhan China College of Science Tianjin University of Technology Tianjin China 

出 版 物：《The Journal of Geometric Analysis》 

年 卷 期：2025年第35卷第3期

页      面：1-47页

摘      要：Monomial polyhedra are a class of bounded singular Reinhardt domains defined as sublevel sets of holomorphic monomials. The purpose of this paper is twofold. We first establish an $$L^p$$ -norm estimate for the Bergman projection on the monomial polyhedra $${\mathcal {U}}_{B}$$ , which can be viewed as a complement of the recent work of the $$L^p$$ regularity for the Bergman projection on monomial polyhedra by Bender et al. (Can J Math 74:732–772, 2022). Then, if $${\mathcal {U}}_{B}$$ is a monomial polyhedron associated to the matrix $$B\in {\mathbb {Z}}^{n\times n}$$ satisfying $$\det \,B=1$$ , we obtain a sharp weighted version of $$L^p$$ -norm estimate for the Bergman projection on $${\mathcal {U}}_{B}$$ .