A reproducing kernel thesis for operators on Bergman-type function spaces

Abstract

In this paper we consider the reproducing kernel thesis for boundedness and compactness for various operators on Bergman-type spaces. In particular, the results in this paper apply to the weighted Bergman space on the unit ball, the unit polydisc and more generally to weighted Fock spaces.

An important issue fixed by replacing the doubling condition with a more flexible finite asymptotic dimension condition

References in corpus (1)

• Products of Toeplitz operators on the Fock space

Cited by in corpus (8)

• Convexity of the Berezin Range
• Compactness of operators on the Bergman space of the Thullen domain
• A Boundedness Criterion for Singular Integral Operators of convolution type on the Fock Space
• A Reproducing Kernel Thesis for Operators on ${\ell }^2$--valued Bergman-type Function Spaces
• On compactness of products of Toeplitz operators
• Compactness of Hankel and Toeplitz operators on convex Reinhardt domains in ${\mathbb{C}}^2$
• Localization and compactness of Operators on Fock Spaces
• Localized Frames and Compactness