Abstract
Closures of weighted Bergman spaces in Bloch type spaces are investigated in the paper. Moreover, the boundedness and compactness of the product of composition and differentiation operators from Bloch type spaces to closures of weighted Bergman spaces spaces in Bloch type spaces are characterized.
Highlights
Let D = {z : |z| < 1} be the open unit disk in the complex plane C and H(D) be the class of all functions analytic in D
For 0 < p < ∞, Hp denotes the Hardy space, which consists of all functions f ∈ H(D) for which
Motivated by the above observations and [7], we naturally look for a characterization of CB(Apω ∩ B)
Summary
Let D = {z : |z| < 1} be the open unit disk in the complex plane C and H(D) be the class of all functions analytic in D. H∞ denotes the space of all bounded analytic functions in D. The Bloch space B is the set of all functions f ∈ H(D) that satisfies f β = sup 1 – |z|2 f (z) < ∞. The little Bloch space, denoted by B0, is the subspace of B consisting of all f ∈ H(D) such that lim|z|→1(1 – |z|2)|f (z)| = 0. Recall that the Bloch type space, denoted by Bα, is the space of all functions f ∈ H(D) satisfying f Bα = f (0) + sup 1 – |z|2 α f (z) < ∞
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