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′.
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Jie Xiao was supported by NSERC (Canada).
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Kotilainen, M., Latvala, V. & Xiao, J. Bloch-Sobolev Spaces and Analytic Composition Operators. Comput. Methods Funct. Theory 5, 381–393 (2006). https://doi.org/10.1007/BF03321105
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DOI: https://doi.org/10.1007/BF03321105