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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.

30D45Bloch functions, normal functions, normal families
30D50Blaschke products, etc. (MSC2000)
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