Reproducing Kernels for Hardy and Bergman Spaces of the Upper Half Plane

Authors : Job BONYO

Pages : 13-23

Doi:10.33434/cams.631112

View : 19 | Download : 6

Publication Date : 2020-03-25

Article Type : Research Paper

Abstract :Using invertible isometries between Hardy and Bergman spaces of the unit disk $\D$ and the corresponding spaces of the upper half plane $\uP$, we determine explicitly the reproducing kernels for the Hardy and Bergman spaces of $\uP$. As a consequence, we obtain the duality relations for the reflexive Hardy and Bergman spaces of the half plane $\uP$.
Keywords : Reproducing kernel, Hardy and Bergman spaces, Bergman projection