# Bloch-Sobolev Spaces and Analytic Composition Operators

Bloch-Sobolev Spaces and Analytic Composition Operators We introduce the so-called Bloch-Sobolev function spaces and show that these spaces have nice closure properties. We also characterize the boundedness and compactness of a composition operator Cø (with analytic symbol ø between two subdomains Ω, Ω′ ⊊ ℝ2) acting between two Bloch-Sobolev spaces. As a by-product we obtain a characterization of those analytic mappings ø: Ω→ Ω′, which are uniformly continuous with respect to the quasihyperbolic metrics in Ω and Ω′. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Computational Methods and Function Theory Springer Journals

# Bloch-Sobolev Spaces and Analytic Composition Operators

, Volume 5 (2) – Mar 7, 2013
13 pages

/lp/springer-journals/bloch-sobolev-spaces-and-analytic-composition-operators-iYchjkNWiJ
Publisher
Springer Journals
Subject
Mathematics; Analysis; Computational Mathematics and Numerical Analysis; Functions of a Complex Variable
ISSN
1617-9447
eISSN
2195-3724
DOI
10.1007/BF03321105
Publisher site
See Article on Publisher Site

### Abstract

We introduce the so-called Bloch-Sobolev function spaces and show that these spaces have nice closure properties. We also characterize the boundedness and compactness of a composition operator Cø (with analytic symbol ø between two subdomains Ω, Ω′ ⊊ ℝ2) acting between two Bloch-Sobolev spaces. As a by-product we obtain a characterization of those analytic mappings ø: Ω→ Ω′, which are uniformly continuous with respect to the quasihyperbolic metrics in Ω and Ω′.

### Journal

Computational Methods and Function TheorySpringer Journals

Published: Mar 7, 2013

### References

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