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.


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)