Criteria for an analytic function belonging to the QK spaces

The author gives a mild integral condition in a nondecreasing function K:[0,∞) → [0,∞), which is sufficient and the best possible to ensure that f is a Bloch function if and only if f belongs to QK, a Möbius-invariant space of functions analytic in the unit disk. Their contributions are slight improvements of known results, and the proofs presented here are independently developed. The corresponding results for meromorphic case are also given.