Area integral means, Hardy and weighted Bergman spaces of planar harmonic mappings

TL;DR

This paper explores properties of planar harmonic mappings, generalizes previous results, examines the relationship between area integral means and harmonic function spaces, and provides coefficient estimates for mappings in weighted Bergman spaces.

Contribution

It extends existing results on harmonic mappings, analyzes their space relationships, and derives new coefficient estimates for weighted Bergman spaces.

Findings

Generalized main results of previous studies

Established links between area integral means and harmonic spaces

Obtained coefficient estimates for weighted Bergman space mappings

Abstract

In this paper, we investigate some properties of planar harmonic mappings. First, we generalize the main results in \cite{CPW3} and \cite{HT}, and then discuss the relationship between area integral means and harmonic Hardy spaces or harmonic weighted Bergman spaces. At the end, coefficient estimates of mappings in weighted Bergman spaces are obtained.