Composition operator on Bloch type spaces

Products of composition and differentiation operators from Zygmund spaces to Bloch spaces and Bers spaces

“…It is interesting to provide a function theoretic characterization for u inducing a bounded or compact composition operator on various spaces (see, e.g. [2,9,10,16,20,23,29,30]). For example, it is well known that C u is bounded on the classical Hardy, Bloch and Bergman spaces.…”

The Bloch space and the dual space of a Luecking-type subspace of

“…We refer to [1,11,14] for more results related to these constructions. Furthermore, the space X 0 is not a subset of the Bloch space.…”

Generalized composition operators on Zygmund spaces and Bloch type spaces

“…Let (z k ) k∈N be a sequence in D such that |ϕ(z k )| → 1 as k → ∞. Let f k be defined by (9), then sup k∈N f k Z < ∞ and f k → 0 uniformly on compact subsets of D as k → ∞. Since C g ϕ : Z → Z is compact, it gives lim k→∞ C g ϕ f k Z = 0.…”

“…Some characterizations of the boundedness and compactness of the composition operator, as well as Volterra type operator, on the Bloch type space and the Zygmund space can be found in [2,6,[8][9][10][13][14][15].…”