On projection from $A^p_\omega$ to the Hardy spaces $H^p$

TL;DR

This paper surveys known results on projecting general weighted holomorphic spaces onto Hardy spaces and introduces a new projection result for the half-plane case.

Contribution

It provides a comprehensive survey of projection results and presents a novel projection theorem for $A^p_ u$ spaces onto $H^p$ in the half-plane.

Findings

Summarizes existing projection results for various domains.

Introduces a new projection theorem for the half-plane case.

Enhances understanding of the relationship between $A^p_ u$ and $H^p$ spaces.

Abstract

This paper describes the known results on the projection from the most general holomorphic spaces $A^p_\omega$, which depend on a functional parameter $\omega$ and are over the unit disc, upper half-plane and the finite complex plane, to the classical Hardy spaces $H^p.$ The paper can be considered as a survey in the mentioned topic. A new result on the projection of the half-plane $A^p_\omega$ to the half-plane Hardy space $H^p$ is obtained.