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 \({\mathcal {U}}_{B}\) .
