Distortion theorems for Bloch functions

Mario Bonk, David Minda and Hiroshi Yanagihara

Vol. 179 (1997), No. 2, 241–262

DOI: 10.2140/pjm.1997.179.241

Abstract

A function f holomorphic on the unit disk 𝔻 is called a Bloch function if

For α ∈ [0,1] let B₁(α) denote the class of Bloch functions which have the normalization ∥f∥_B ≤ 1, f(0) = 0 and f′(0) = α. A type of subordination theorem is established for B₁(α). This theorem yields numerous sharp growth, distortion, curvature and covering theorems for B₁(α).

Milestones

Received: 1 September 1995

Published: 1 June 1997