Reproducing Kernels and Radial Differential Operators for Holomorphic and Harmonic Besov Spaces on Unit Balls: a Unified View

We investigate some relations between the reproducing kernels of Hilbert spaces of holomorphic and harmonic functions on the unit balls and the radial differential operators acting on the spaces that allow their characterization via integrals of their derivatives on the balls. We compare and contrast the holomorphic and harmonic cases.