Bulletin of the Australian Mathematical Society

Research Article

The n-th derivative characterisation of Möbius invariant Dirichlet space

Rauno Aulaskaria1, Maria Nowaka2 and Ruhan Zhaoa3

a1 University of Joensuu, PO Box 111, FIN-8010 Joensuu, Finland e-mail: aulaskari@joyl.joensuu.fi

a2 Institute of Mathematics, Maria Curie-Sklodowska University, pl. M. Curie-Skodowskiej 1, 20–031 Lublin, Poland

a3 University of Joensuu, PO Box 111, FIN-8010 Joensuu, Finland

Abstract

In this paper we give the n-th derivative criterion for functions belonging to recently defined function spaces Qp and Qp, 0. For a special parameter value p = 1 this criterion is applied to BMOA and VMOA, and for p > 1 it is applied to the Bloch space S0004972700031993_inline1 and the little Bloch space S0004972700031993_inline2. Further, a Carleson measure characterisation is given to Qp, and in the last section the multiplier space from Hq into Qp is considered.

(Received November 24 1997)