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

Year 2020, Volume: 3 Issue: 1, 13 - 23, 25.03.2020

Job BONYO

https://doi.org/10.33434/cams.631112

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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