Weighted composition operators from Bloch-type into Bers-type spaces

In this paper we consider the weighted composition operator uC_{\varphi} from Bloch-type space B^{\alpha} into Bers-type space H_{\beta}^{\infty}, in three cases, \alpha>1, \alpha=1 and \alpha<1. We give the necessary and sufficient conditions for boundedness and compactness of the above operator.

Composition Operator, Boundedness, Compactness, Hyperbolic Bloch-Type Space βμ∗, Hyperbolic-Type Space

In this paper, we obtain some characterizations of composition operators Cφ, which are induced by an analytic self-map φ of the unit disk Δ, from hyperbolic Bloch type space βμ∗ into hyperbolic type space QK,p,q∗.

POWERS OF COMPOSITION OPERATORS: ASYMPTOTIC BEHAVIOUR ON BERGMAN, DIRICHLET AND BLOCH SPACES

We study the asymptotic behaviour of the powers of a composition operator on various Banach spaces of holomorphic functions on the disc, namely, standard weighted Bergman spaces (finite and infinite order), Bloch space, little Bloch space, Bloch-type space and Dirichlet space. Moreover, we give a complete characterization of those composition operators that are similar to an isometry on these various Banach spaces. We conclude by studying the asymptotic behaviour of semigroups of composition operators on these various Banach spaces.