- Communications in Advanced Mathematical Sciences
- Vol: 3 Issue: 1
- Reproducing Kernels for Hardy and Bergman Spaces of the Upper Half Plane
Reproducing Kernels for Hardy and Bergman Spaces of the Upper Half Plane
Authors : Job Bonyo
Pages : 13-23
Doi:10.33434/cams.631112
View : 10 | Download : 6
Publication Date : 2020-03-25
Article Type : Research
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