BMO, VMO and Hankel operators on the Bergman space of strongly pseudoconvex domains
type: Item
instance of: scholarly article
title: BMO, VMO and Hankel operators on the Bergman space of strongly pseudoconvex domains
zbMATH Open document ID: 0793.47025
DOI: 10.1016/0022-1236(92)90054-M
author: Huiping Li
published in: Journal of Functional Analysis
publication date: 1992-08-13T00:00:00Z
review text: For a bounded pseudoconvex domain \(D\) with smooth boundary in \(\mathbb{C}^ n\), the author considers Hankel operators \(H_ f\) acting on the Bergmann space \(H^ 2(D)\), consisting of the holomorphic \(L^ 2\) functions on \(D\). For \(f\in L^ 2(D)\), he proves that \(H_ f\) and \(H_{\bar f}\) are bounded provided that \(f\) has ``bounded mean oscillation'' on \(D\) (in the sense that he defines), and that \(H_ f\), \(H_{\bar f}\) are compact if \(f\) has ``vanishing mean oscillation at the boundary of \(D\)''. For \(f\in H^ 2(D)\), these conditions are also necessary. Analogous results for bounded symmetric domains were proved by \textit{D. Békollé}, \textit{C. A. Berger}, \textit{L. A. Coburn} and \textit{K. H. Zhu} [J. Funct. Anal. 93, 310-350 (1990; Zbl 0765.32005)], and the present results partially answer a conjecture posed at the end of that paper.
Mathematics Subject Classification ID: 47B35
Mathematics Subject Classification ID: 32T99
Mathematics Subject Classification ID: 32A37
zbMATH DE Number: 40704
zbMATH Keywords: vanishing mean oscillation at the boundary
zbMATH Keywords: bounded mean oscillation
zbMATH Keywords: bounded pseudoconvex domain
zbMATH Keywords: Hankel operators
zbMATH Keywords: Bergmann space
reviewed by: Jeffrey R. Butz
MaRDI profile type: Publication
cites work: The comparability of the Kobayashi approach region and the admissible approach region
cites work: BMO in the Bergman metric on bounded symmetric domains
cites work: Function Theory on Cartan Domains and the Berezin-Toeplitz Symbol Calculus
cites work: Q3480376
cites work: Comparison of the Bergman and the Kobayashi metric
cites work: The Bergman kernel and biholomorphic mappings of pseudoconvex domains
cites work: Boundary behavior of the Carathéodory, Kobayashi, and Bergman metrics on strongly pseudoconvex domains in {{𝐂}}ⁿ with smooth boundary
cites work: Boundary Behavior of the Caratheodory and Kobayashi Metrics on Strongly Pseudoconvex Domains in C n with Smooth Boundary
cites work: Q3315776
cites work: Q4171170
cites work: INTEGRAL REPRESENTATIONS OF FUNCTIONS HOLOMORPHIC IN STRICTLY PSEUDO-CONVEX DOMAINS AND SOME APPLICATIONS
cites work: Boundary properties of holomorphic functions of several complex variables
cites work: Optimal Lipschitz and \(L^p\) regularity for the equation \(\overline\partial u=f\) on strongly pseudo-convex domains
cites work: Q3924489
cites work: Q3764429
cites work: Q3764425
cites work: La métrique de Kobayashi et la représentation des domaines sur la boule
cites work: A Technique for Characterizing Carleson Measures on Bergman Spaces
cites work: Estimates for the Bergman and Szegö projections on strongly pseudo-convex domains
cites work: Q3719028
cites work: Bloch functions in several complex variables. II.
cites work: Comparison Between the Kobayashi and Caratheodory Distances on Strongly Pseudoconvex Bounded Domains in C n
cites work: Fredholm operators associated with strongly pseudoconvex domains in \(C^n\)
cites work: Q3873024
description: scientific article; zbMATH DE number 40704