A Reproducing Kernel Thesis for Operators on ${\ell }^2$--valued Bergman-type Function Spaces

Abstract

In this paper we consider the reproducing kernel thesis for boundedness and compactness for operators on ${\ell }^2$--valued Bergman-type spaces. This paper generalizes many well--known results about classical function spaces to their ${\ell }^2$--valued versions. In particular, the results in this paper apply to the weighted ${\ell }^2$--valued Bergman space on the unit ball, the unit polydisc and, more generally to weighted Fock spaces.

In order to be self contained, this paper draws from arXiv:1204.5548, arXiv:1407.4786

References in corpus (2)

• A reproducing kernel thesis for operators on Bergman-type function spaces
• The Essential Norm of Operators on $A^p({\mathbb{D}}^n)$