Let 0 ≤ α < 1. Denote the open unit polydisk in C by ∆. We obtain a purely function-theoretic condition characterizing the holomorphic self-maps of ∆ that induce bounded composition operators on (1−α)-Bloch spaces, which we define on ∆. As a consequence, we extend Madigan’s characterization of bounded composition operators on analytic α-Lipschitz spaces over ∆ for 0 < α < 1 to an analogous char...

The boundedness and compactness of the integral-type operator Luðf ÞðzÞ 1⁄4 Z 1 0 Rf ðuðtzÞÞgðtzÞ dt t ; z 2 B; where g is a holomorphic function on the open unit ball B in C such that g(0) = 0 and u is a holomorphic self-map of B, from Bloch-type spaces Bl and Bl;0, where l is a normal weight, to F(p,q,s) space on B are characterized, solving a recent open problem. 2011 Elsevier Inc. All right...

Natural metrics in the hyperbolic α-Bloch-, weighted Dirichletand Qp-classes are introduced, and these classes are shown to be complete metric spaces with respect to the corresponding metrics. Then Lipschitz continuous and compact composition operators Cφ(f) = f ◦φ acting from the hyperbolic α-Bloch-class to the hyperbolic weighted Dirichletor Qp-class are characterized by conditions depending ...

and Applied Analysis 3 Here H∞ ω denotes the weighted-type space consisting of all f ∈ H B with ∥ ∥f ∥ ∥ H∞ ω sup z∈B ω z ∣ ∣f z ∣ ∣ < ∞ 1.9 see, e.g., 23, 24 . Associated weights assist us in studying of weighted-type spaces of holomorphic functions. It is known that associated weights are also continuous, 0 < ω ≤ ω̃, and for each z ∈ B, we can find an fz ∈ H∞ ω , ‖fz‖H∞ ω ≤ 1 such that fz z 1/...

In this paper, motivated by Qian, et al [20, 22], we give a new characterization for the closure of space Ds in Bloch space.

First, we introduce some basic notation which is used in this paper. Throughout the entire paper, the unit disk in the finite complex plane C will be denoted by D. H D will denote the space of all analytic functions on D. Every analytic self-map φ of the unit disk D induces through composition a linear composition operator Cφ fromH D to itself. It is a well-known consequence of Littlewood’s sub...