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