Journal Home Page Cumulative Index List of all Volumes Complete Contentsof this Volume Previous Article Next Article Computational Methods and Function Theory 5 (2005), No. 2, 381--393 Copyright Heldermann Verlag 2005 Bloch-Sobolev Spaces and Analytic Composition Operators Marko Kotilainen marko.kotilainen@joensuu.fi , Department of Mathematics, University of Joensuu, P.O. Box 111, FIN-80101 Joensuu, Finland. Visa Latvala visa.latvala@joensuu.fi , Department of Mathematics, University of Joensuu, P.O. Box 111, FIN-80101 Joensuu, Finland. Jie Xiao jxiao@math.mun.ca , Department of Mathematics and Statistics, Memorial University of Newfoundland, St. John's, NL, A1C5S7, Canada. [Abstract-pdf] [Abstract-ps] 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 $C_\phi$ (with analytic symbol $\phi$ between two subdomains $\Omega, \Omega'\subsetneq \mathbb{R}^2$) acting between two Bloch-Sobolev spaces. As a by-product we obtain a characterization of those analytic mappings $\phi\colon\Omega\to\Omega'$, which are uniformly continuous with respect to the quasihyperbolic metrics in $\Omega$ and $\Omega'$. Keywords: Bloch-Sobolev spaces, composition operators, analytic mappings. MSC 2000: Primary 31B05; Secondary 46E15, 47B38. [FullText-pdf (285 K)] [FullText-ps (482 K)]