About this Journal Submit a Manuscript Table of Contents
Abstract and Applied Analysis
Volume 2012 (2012), Article ID 647972, 9 pages
http://dx.doi.org/10.1155/2012/647972
Research Article

Schwarz-Pick Estimates for Holomorphic Mappings with Values in Homogeneous Ball

Department of Mathematics, Zhejiang Normal University, Zhejiang, Jinhua 321004, China

Received 11 July 2012; Accepted 21 October 2012

Academic Editor: Abdelghani Bellouquid

Copyright © 2012 Jianfei Wang. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. St. Ruscheweyh, “Two remarks on bounded analytic functions,” Serdica, vol. 11, no. 2, pp. 200–202, 1985. View at Zentralblatt MATH
  2. P. Ghatage, J. Yan, and D. Zheng, “Composition operators with closed range on the Bloch space,” Proceedings of the American Mathematical Society, vol. 129, no. 7, pp. 2039–2044, 2001. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  3. B. D. MacCluer, K. Stroethoff, and R. Zhao, “Generalized Schwarz-Pick estimates,” Proceedings of the American Mathematical Society, vol. 131, no. 2, pp. 593–599, 2003. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  4. F. G. Avkhadiev and K.-J. Wirths, “Schwarz-Pick inequalities for derivatives of arbitrary order,” Constructive Approximation, vol. 19, no. 2, pp. 265–277, 2003. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  5. P. Ghatage and D. Zheng, “Hyperbolic derivatives and generalized Schwarz-Pick estimates,” Proceedings of the American Mathematical Society, vol. 132, no. 11, pp. 3309–3318, 2004. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  6. S. Dai and Y. Pan, “Note on Schwarz-Pick estimates for bounded and positive real part analytic functions,” Proceedings of the American Mathematical Society, vol. 136, no. 2, pp. 635–640, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  7. J. M. Anderson, M. A. Dritschel, and J. Rovnyak, “Schwarz-Pick inequalities for the Schur-Agler class on the polydisk and unit ball,” Computational Methods and Function Theory, vol. 8, no. 1-2, pp. 339–361, 2008. View at Zentralblatt MATH
  8. Z. H. Chen and Y. Liu, “Schwarz-Pick estimates for bounded holomorphic functions in the unit ball of Cn,” Acta Mathematica Sinica, vol. 26, no. 5, pp. 901–908, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  9. S. Dai, H. Chen, and Y. Pan, “The Schwarz-Pick lemma of high order in several variables,” Michigan Mathematical Journal, vol. 59, no. 3, pp. 517–533, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  10. S. Dai, H. Chen, and Y. Pan, “The high order Schwarz-Pick lemma on complex Hilbert balls,” Science China, vol. 53, no. 10, pp. 2649–2656, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  11. S. G. Krantz, Function Theory of Several Complex Variables, John Wiley & Sons, New York, NY, USA, 1982.
  12. S. Gong, Convex and Starlike Mappings in Several Complex Variables, vol. 435 of Mathematics and its Applications (China Series), Kluwer Academic Publishers, Dordrecht, The Netherlands, 1998. View at Publisher · View at Google Scholar