Boundary behavior of the Szegö kernel. Issue 1 (6th March 2022)

• Record Type: Journal Article
• Authors: Wu, JuJie; Xing, Xu
• Is Part Of: Bulletin of the London Mathematical Society. Volume 54:Issue 1(2022)
• Page Start: 285
• Page End: 300
• Publication Date: 2022-03-06
• Subjects: Mathematics -- Periodicals; 510
• DOI: 10.1112/blms.12623
• Languages: English
• ISSNs: 0024-6093

Abstract

Abstract: We give a Hörmander‐type localization principle for the diagonal Szegö kernel S Ω ( z ) $S_\Omega (z)$ . We also show that for each boundary point z 0 $z_0$, S Ω ( z ) ≳ | z − z 0 | − 1 3 $S_\Omega (z)\gtrsim |z-z_0|^{-\frac{1}{3}}$ holds non‐tangentially for any bounded pseudoconvex domain with smooth boundary in C 2 ${\mathbb {C}}^2$ .