Boundary behavior of the Szegö kernel

2021/06/06 by Jujie Wu, Xing Xu, Xu Xing
Mathematics · #Algebraic and Geometric Analysis #Analytic and geometric function theory #Boundary (topology) #Bounded function #Combinatorics #Domain (mathematical analysis) #Geology #Geometry #Heat kernel #Holomorphic and Operator Theory #Kernel (algebra) #Mathematical analysis #Mathematics #Omega #Physics #Point (geometry) #Pure mathematics #Type (biology) #math.CV

paper · pdf · doi:10.1112/blms.12623

arxiv created 2021/06/06 · openalex publication_date 2022/02/01 · arxiv updated 2022/03/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

We give a Hörmander-type localization principle for the Szegö kernel S_Ω(z). We also show that for each boundary point z₀, S_Ω(z)\gtrsim|z-z₀|^-(1)/(3) holds non-tangentially for any bounded pseudoconvex domain with smooth boundary in \mathbb C².

Citations

• Function Theory of Several Complex Variables
• L2 estimates and existence theorems for the ∂ operator
• The Bergman kernel and biholomorphic mappings of pseudoconvex domains
• On the extension ofL 2 holomorphic functions
• An Example of a Smooth Linear Partial Differential Equation Without Solution