A distortion theorem and the Bloch constant for Bloch mappings in ℂN
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Let BX be a homogeneous unit ball in X = ℂn. In this paper, we generalize Bonk’s distortion theorem to Bloch mappings on BX. As an application, we give a lower bound of the Bloch constant.
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- C.-H. Chu, Jordan Structures in Geometry and Analysis, Cambridge Tracts in Mathematics, Vol. 190, Cambridge University Press, Cambridge, 2012.Google Scholar
- L. A. Harris, Bounded symmetric homogeneous domains in infinite dimensional spaces, in Proceedings on Infinite Dimensional Holomorphy, Internat. Conf., Univ. Kentucky, Lexington, KY, 1973, Lecture Notes in Mathematics, Vol. 364, Springer, Berlin, 1974, pp. 13–40.Google Scholar
- L. K. Hua, Harmonic Analysis of Functions of Several Complex Variables in the Classical Domains, Translations of Mathematical Monographs, Vol. 6, American Mathematical Society, Providence, RI, 1963.Google Scholar
- W. Kaup, A Riemann mapping theorem for bounded symmetric domains in complex Banach spaces, Math. Z. 183 (1983), 503–529.Google Scholar
- W. Kaup, Hermitian Jordan triple systems and the automorphisms of bounded symmetric domains, in Mathematics and Its Applications, Vol. 303, Springer, Dordrecht, 1994, pp. 204–214.Google Scholar
- O. Loos, Bounded Symmetric Domains and Jordan Pairs, University of California, Irvine, 1977.Google Scholar
- G. Roos, Jordan triple systems, in Analysis and Geometry on Complex Homogeneous Domains, in Progress in Mathematics, Vol. 185, Birkhäuser Boston, Inc., Boston, MA, 2000, pp. 425–534.Google Scholar
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