On a class of quasiconformal functions in Banach spaces
HTML articles powered by AMS MathViewer
- by Su Shing Chen PDF
- Proc. Amer. Math. Soc. 37 (1973), 545-548 Request permission
Abstract:
A quasiconformal function f on a domain D in a complex Banach space E is defined as a function on D such that for every holomorphic mapping $\Phi$ from the unit disk $\Delta$ into D the composite mapping $f \circ \Phi$ is quasiconformal in the usual sense. With respect to the Kobayashi-Kiernan pseudo distance on D, Schwarz’s lemma, Liouville’s theorem and the little Picard theorem are obtained for quasiconformal functions. A maximum modulus principle is also obtained for quasiconformal functions.References
- Lars V. Ahlfors, Lectures on quasiconformal mappings, Van Nostrand Mathematical Studies, No. 10, D. Van Nostrand Co., Inc., Toronto, Ont.-New York-London, 1966. Manuscript prepared with the assistance of Clifford J. Earle, Jr. MR 0200442
- Einar Hille and Ralph S. Phillips, Functional analysis and semi-groups, American Mathematical Society Colloquium Publications, Vol. 31, American Mathematical Society, Providence, R.I., 1957. rev. ed. MR 0089373
- Sin Hitotumatu, On quasi-conformal functions of several complex variables, J. Math. Mech. 8 (1959), 77–94. MR 0102608, DOI 10.1512/iumj.1959.8.58005
- Peter J. Kiernan, Quasiconformal mappings and Schwarz’s lemma, Trans. Amer. Math. Soc. 148 (1970), 185–197. MR 255807, DOI 10.1090/S0002-9947-1970-0255807-6
- Shoshichi Kobayashi, Hyperbolic manifolds and holomorphic mappings, Pure and Applied Mathematics, vol. 2, Marcel Dekker, Inc., New York, 1970. MR 0277770
- Leopoldo Nachbin, Topology on spaces of holomorphic mappings, Ergebnisse der Mathematik und ihrer Grenzgebiete, Band 47, Springer-Verlag New York, Inc., New York, 1969. MR 0254579
Additional Information
- © Copyright 1973 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 37 (1973), 545-548
- MSC: Primary 32H15; Secondary 32K05
- DOI: https://doi.org/10.1090/S0002-9939-1973-0318518-2
- MathSciNet review: 0318518