# Composition operators: ${N}_{\alpha }$ to the Bloch space to ${Q}_{\beta }$

Studia Mathematica (2000)

• Volume: 139, Issue: 3, page 245-260
• ISSN: 0039-3223

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## Abstract

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Let ${N}_{\alpha }$,B and Qβ be the weighted Nevanlinna space, the Bloch space and the Q space, respectively. Note that B and ${Q}_{\beta }$ are Möbius invariant, but ${N}_{\alpha }$ is not. We characterize, in function-theoretic terms, when the composition operator ${C}_{\varphi }f=f◦\varphi$ induced by an analytic self-map ϕ of the unit disk defines an operator ${C}_{\varphi }:{N}_{\alpha }\to B$, $B\to {Q}_{\beta }$, ${N}_{\alpha }\to {Q}_{\beta }$ which is bounded resp. compact.

## How to cite

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Xiao, Jie. "Composition operators: $N_α$ to the Bloch space to $Q_β$." Studia Mathematica 139.3 (2000): 245-260. <http://eudml.org/doc/216721>.

@article{Xiao2000,
abstract = {Let $N_α$,B and Qβ be the weighted Nevanlinna space, the Bloch space and the Q space, respectively. Note that B and $Q_β$ are Möbius invariant, but $N_α$ is not. We characterize, in function-theoretic terms, when the composition operator $C_ϕ f=f◦ϕ$ induced by an analytic self-map ϕ of the unit disk defines an operator $C_ϕ:N_α→B$, $B→Q_β$, $N_α→Q_β$ which is bounded resp. compact.},
author = {Xiao, Jie},
journal = {Studia Mathematica},
keywords = {composition operator; boundedness; compactness; $N_α$; β; Q\_β; weighted Nevanlinna space; Bloch space; space; Bloch function; Carleson box; Möbius invariant version of the generalized Nevanlinna counting function},
language = {eng},
number = {3},
pages = {245-260},
title = {Composition operators: $N_α$ to the Bloch space to $Q_β$},
url = {http://eudml.org/doc/216721},
volume = {139},
year = {2000},
}

TY - JOUR
AU - Xiao, Jie
TI - Composition operators: $N_α$ to the Bloch space to $Q_β$
JO - Studia Mathematica
PY - 2000
VL - 139
IS - 3
SP - 245
EP - 260
AB - Let $N_α$,B and Qβ be the weighted Nevanlinna space, the Bloch space and the Q space, respectively. Note that B and $Q_β$ are Möbius invariant, but $N_α$ is not. We characterize, in function-theoretic terms, when the composition operator $C_ϕ f=f◦ϕ$ induced by an analytic self-map ϕ of the unit disk defines an operator $C_ϕ:N_α→B$, $B→Q_β$, $N_α→Q_β$ which is bounded resp. compact.
LA - eng
KW - composition operator; boundedness; compactness; $N_α$; β; Q_β; weighted Nevanlinna space; Bloch space; space; Bloch function; Carleson box; Möbius invariant version of the generalized Nevanlinna counting function
UR - http://eudml.org/doc/216721
ER -

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