Bulletin of the Australian Mathematical Society

Research Article

Besov-type characterisations for the Bloch space

Karel Stroethoffa1

a1 Department of Mathematical Sciences, University of Montana, Missoula, Montana 59801, United States of America.

Abstract

We will prove local and global Besov-type characterisations for the Bloch space and the little Bloch space. As a special case we obtain that the Bloch space consists of those analytic functions on the unit disc whose restrictions to pseudo-hyperbolic discs (of fixed pseudo-hyperbolic radius) uniformly belong to the Besov space. We also generalise the results to Bloch functions and little Bloch functions on the unit ball in S0004972700003324_inline1. Finally we discuss the related spaces BMOA and VMOA.

(Received July 27 1988)