# 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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topXiao, 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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