Abstract
In this paper, we characterize the closure of the Morrey space in the Bloch space. Furthermore, the boundedness and compactness of composition operators from the Bloch space to the closure of the Morrey space in the Bloch space are investigated.
Highlights
Let D = {z : |z| < 1} be the open unit disk in the complex plane C and H(D) be the space of analytic functions on D
The little Bloch space B0 consists of all f ∈ H(D) such that lim
It is a simple consequence of the Schwartz-Pick lemma that any analytic self-mapping φ of D induces a bounded composition operator Cφ on the Bloch space
Summary
The little Bloch space B0 consists of all f ∈ H(D) such that lim f (reiθ)p dθ Denote by H∞ = H∞(D) the space of bounded analytic functions on D. From [2] or [3], the norm of functions f ∈ L2,λ(D) can be defined as follows. It is a simple consequence of the Schwartz-Pick lemma that any analytic self-mapping φ of D induces a bounded composition operator Cφ on the Bloch space.
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