The n-th derivative characterisation of mobius invariant Dirichlet space

In this paper we give the n-th derivative criterion for functions belonging to recently defined function spaces Q(p) and Q(p,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 beta and the little Bloch space beta(0). Further, a Carleson measure characterisation is given to Q(p), and in the last section the multiplier space from H-q into Q(p) is considered.