Growth of Holomorphic Functions in Banach Function Space and in Weighted Bergman Spaces as a Special Case

The paper establishes growth estimates near the boundary for holomorphic functions on the unit disc and the upper half-plane. General results are formulated for Banach function spaces (BFS). As a primary result, we provide estimates for holomorphic functions in weighted Lebesgue spaces with a radial weight on the disc and a weight depending on the vertical variable on the half-plane. The article arose as a systematization of estimates from our earlier work, and we consider the results for the half-plane to be the core of the present paper.