Reproducing Kernels for hardy and Bergman spaces of the upper half plane - Bonyo, Job (Strathmore University, 2019)
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.
Paper presented at the 5th Strathmore International Mathematics Conference (SIMC 2019), 12 - 16 August 2019, Strathmore University, Nairobi, Kenya
Keywords: Analytic functions; Reproducing kernel; Hardy and Bergrnan spaces; Bergman projection; Duality; Szegö projection