The Essential Norm of Operators on $$\ell ^{2}$$ ℓ 2 -Valued Bergman-Type Function Spaces

Abstract

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