We present some characterizations for the compactness of difference two composition operators acting between analytic Besov spaces and weighted little Bloch type space over unit disk.

The characterization by weighted Lipschitz continuity is given for the Bloch space on the unit ball of Rn. Similar results are obtained for little Bloch and Besov spaces.

Let u be a holomorphic function and φ a holomorphic self-map of the open unit disk D in the complex plane. We give some new characterizations for the boundedness of the weighted composition operators uCφ from Bloch type spaces to Zygmund type spaces in D in terms of u,φ, their derivatives and the n-th power φ of φ. Moreover, we obtain some similar estimates for their essential norms. From which...

and Applied Analysis 3 2. Main Results and Proofs In this section, we give our main results and their proofs. Before stating these results, we need some auxiliary results, which are incorporated in the lemmas which follows. Lemma 2.1. Assume that g ∈ H Bn and μ : Bn → 0,∞ are normal. Then Tg : H∞ log → Bμ is compact if and only if Tg : H∞ log → Bμ is bounded and for any bounded sequence fk k∈N ...