Premium
Sharp Distortion Estimate for Locally Schlicht Bloch Functions
Author(s) -
Yanagihara Hiroshi
Publication year - 1994
Publication title -
bulletin of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.396
H-Index - 48
eISSN - 1469-2120
pISSN - 0024-6093
DOI - 10.1112/blms/26.6.539
Subject(s) - mathematics , bloch space , distortion (music) , space (punctuation) , unit (ring theory) , mathematical analysis , pure mathematics , combinatorics , compact space , telecommunications , linguistics , philosophy , mathematics education , amplifier , bandwidth (computing) , computer science
Let B ∞ be the space of locally schlicht Bloch functions f which are analytic in the unit disc Δ with f (0) = f ′(0) − 1 = 0 satisfying 0 < | f ′( z )|(1 − | z | 2 ) ⩽ 1. For each fixed z 0 ∈ Δ we shall determine the shape of the set {log f ′( z 0 ): f ∈B ∞ }, that is, we shall give the sharp distortion estimate for locally schilcht Bloch functions.