On composition operators in QK type spaces

Abstract

Let p≥1, q>-2 and let K:[0,∞)→[0,∞) be nondecreasing. With a different choice of p, q, K, the Banach space QK(p,q) coincides with many well-known analytic function spaces. Boundedness and compactness of the composition operator Cφ from α-Bloch space Bα into QK(p,q) are characterized by a condition depending only on analytic mapping φ:𝔻→𝔻. The same properties are also studied in the case Cφ:QK(p,q)→Bα.