Landau-Bloch constants for functions in $\alpha$-Bloch spaces and Hardy spaces

TL;DR

This paper establishes sharp distortion and Landau's theorems for functions in $\u03b1$-Bloch and Hardy spaces, generalizing previous results and confirming the existence of Landau-Bloch constants.

Contribution

It provides new sharp distortion theorems and Landau's theorems for $\u03b1$-Bloch and Hardy space functions, extending classical results.

Findings

Sharp distortion theorem for $\u03b1$-Bloch space functions

Landau's theorem for $\u03b1$-Bloch space functions

Existence of Landau-Bloch constants in Hardy spaces

Abstract

In this paper, we obtain a sharp distortion theorem for a class of functions in $\alpha$-Bloch spaces, and as an application of it, we establish the corresponding Landau's theorem. These results generalize the corresponding results of Bonk, Minda and Yanagihara, and Liu, respectively. We also prove the existence of Landau-Bloch constant for a class of functions in Hardy spaces and the obtained result is a generalization of the corresponding result of Chen and Gauthier.