Pseudo-Carleson Measures for Fock Spaces

Abstract

In this paper, we introduce pseudo-Carleson measure, a generalization of Carleson measure, for Fock spaces, and give sufficient and necessary conditions for a complex Borel measure to be pseudo-Carleson. We then give integral representations of functions in a Fock space, and use the measures to characterize boundedness and compactness of small Hankel operators on Fock spaces.