The Bergman projection and weighted C^k estimates for the canonical solution to \dbar on non-smooth domains

2009/03/24 by Dariush Ehsani, Ehsani, Dariush
Mathematics · #32A25 #32W05 #Algebraic and Geometric Analysis #Complex Variables (math.CV) #FOS: Mathematics #Holomorphic and Operator Theory #Meromorphic and Entire Functions #math.CV #msc:32A25 #msc:32W05

paper · pdf · doi:10.48550/arxiv.0903.4087

19 pages

arxiv created 2009/03/24 · openalex publication_date 2009/03/24 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We apply integral representations for functions on non-smooth strictly pseudoconvex domains, the Henkin-Leiterer domains, to derive weighted C^k estimates for the component of a given function, f, which is orthogonal to holomorphic functions in terms of C^k norms of \mdbar f. The weights are powers of the gradient of the defining function of the domain.

Related

• Weighted C^k estimates for a class of integral operators on non-smooth domains
• Principal parts of operators in the dbar-Neumann problem on strictly pseudoconvex non-smooth domains
• Weighted Bergman spaces and the ∂-equation
• Estimates of the L^p norms of the Bergman projection on strongly pseudoconvex domains
• Weighted estimates of the Bergman projection with matrix weights