The reproducing formula with fractional orders on the parabolic Bloch space

Abstract

In this paper, we study the reproducing formula with fractional orders on the parabolic Bloch space. As an application of the reproducing formula, we characterize the dual and pre-dual spaces of parabolic Bergman spaces. Furthermore, we generalize the integral pairing, which gives the duality between the parabolic Bloch space and the parabolic Bergman space.