On Boundedness of Bergman Projection Operators in Banach Spaces of Holomorphic Functions in Half-Plane and Harmonic Functions in Half-Space

Abstract

We present a simple proof of the boundedness of holomorphic and harmonic Bergman projection operators on a half-plane and a half-space respectively on the Orlicz space, the variable exponent Lebesgue space, and the variable exponent generalized Morrey space. The approach is based on an idea due to V. P. Zaharyuta and V. I. Yudovich (1962) to use Calderón–Zygmund operators for proving the boundedness of the Bergman projection in Lebesgue spaces on the unit disc. We also study the rate of growth of functions near the boundary in the spaces under consideration.