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.