Abstract

We give a criterion for q-valent analytic functions in the unit disk to belong to QK, a Möbius-invariant space of functions analytic in the unit disk in the plane for a nondecreasing function K:[0,∞)→[0,∞), and we show by an example that our condition is sharp. As corollaries, classical results on univalent functions, the Bloch space, BMOA, and Qp spaces are obtained.