BMO, VMO and Hankel operators on the Bergman space of strongly pseudoconvex domains

BMO ON STRONGLY PSEUDOCONVEX DOMAINS: HANKEL OPERATORS, DUALITY AND a-ESTIMATES

We study the condition that characterizes the symbols of bounded Hankel operators on the Bergman space of a strongly pseudoconvex domain and show that it is equivalent to BMO plus analytic. (Here we mean the Bergman metric BMO of Berger, Coburn and Zhu.) In the course of the proof we obtain new d -estimates that may be of independent interest. Some applications include a decomposition of BMO si...

Schatten Class Hankel Operators on the Bergman Spaces of Strongly Pseudoconvex Domains

In this paper, we characterize holomorphic functions / such that the Hankel operators Hj are in the Schatten classes on bounded strongly pseudoconvex domains. It is proved that for p > In , Hj is in the Schatten class Sp if and only if / is in the Besov space Bp ; for p < In , Hj is in the Schatten class Sp if and only if / = constant.

Hankel Operators on the Bergman Space of Bounded Symmetric Domains

Let ii be a bounded symmetric domain in C with normalized 2 volume measure dV . Let P be the orthogonal projection from L (il, dV) 2 2 onto the Bergman space La(Q) of holomorphic functions in L (ii, dV). Let P be the orthogonal projection from L (ii, dV) onto the closed subspace of antiholomorphic functions in L (ii, dV). The "little" Hankel operator h, with symbol / is the operator from La(Ci)...

Intermediate Hankel Operators on the Bergman Space

Hankel Operators and the Dixmier Trace on Strictly Pseudoconvex Domains

Generalizing earlier results for the disc and the ball, we give a formula for the Dixmier trace of the product of 2n Hankel operators on Bergman spaces of strictly pseudoconvex domains in C. The answer turns out to involve the dual Levi form evaluated on boundary derivatives of the symbols. Our main tool is the theory of generalized Toeplitz operators due to Boutet de Monvel and Guillemin. 2000...