Composition operators in generalized Hölder classes of analytic functions in the unit disc

We study composition operators in Hölder analytic classes (constructed by means of modulus of continuity) as well as in classes of varying hölderity. For these operators, boundedness and compactness conditions are obtained in various terms (in particular, in terms that do not use the derivative). Characterization of embeddings of the classes under consideration and characteristics of functions from these classes are especially investigated.