Hankel operators on the Bergman space of bounded symmetric domains

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

Finite Rank Intermediate Hankel Operators on the Bergman Space

In this paper we characterize the kernel of an intermediate Hankel operator on the Bergman space in terms of the inner divisors and obtain a characterization for finite rank intermediate Hankel operators.

Toeplitz and Hankel Operators on a Vector-valued Bergman Space

In this paper, we derive certain algebraic properties of Toeplitz and Hankel operators defined on the vector-valued Bergman spaces L2,C n a (D), where D is the open unit disk in C and n ≥ 1. We show that the set of all Toeplitz operators TΦ,Φ ∈ LMn(D) is strongly dense in the set of all bounded linear operators L(L2,Cn a (D)) and characterize all finite rank little Hankel operators.

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.