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The n-th derivative characterisation of Möbius invariant Dirichlet space. (English) Zbl 1157.30318
Summary: 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 B and the little Bloch space B 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.
MSC:
30D45Bloch functions, normal functions, normal families
30D50Blaschke products, etc. (MSC2000)