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Using invertible isometries between Hardy and Bergman spaces of the unit disk D and the corresponding spaces of the upper half plane U, we determine explicitly the reproducing kernels for the Hardy and Bergman spaces of U. As a consequence, we obtain the duality relations for the reflexive Hardy and Bergman spaces of the half plane U.

Dedicated to Prof. Len Miller (PhD advisor to J. O. Bonyo) and Prof. Vivien Miller of Mississippi State University on their retirement