Skip to main content
SpringerLink
Log in

A note on Schwarz-Pick estimate

  • Published:
Chinese Annals of Mathematics, Series B Aims and scope Submit manuscript

Abstract

A Schwarz-Pick estimate of higher order derivative for holomorphic functions with positive real part on B n is presented. This improves the earlier work on Schwarz-Pick estimate of higher order derivatives for holomorphic functions with positive real part on the unit disk in ℂ.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Anderson, J. M., Dritschel, M. A. and Rovnyak, J., Schwarz-Pick inequalities for the Schur-Agler class on the polydisk and unit ball, Comput. Meth. Funct. Theory, 8(2), 2008, 339–361.

    MATH  MathSciNet  Google Scholar 

  2. Boas H. P., Majorant series, J. Korean Math. Soc., 37, 2000, 321–337.

    MATH  MathSciNet  Google Scholar 

  3. Chen, Z. H. and Liu, Y., Schwarz-Pick estimates for bounded holomorphic functions in the unit ball of ℂn, Acta Math. Sin. Ser. B, in press.

  4. Dai, S. Y., Chen, H. H. and Pan, Y. F., The Schwarz-Pick lemma of high order in several variables, preprint.

  5. Dai, S. Y. and Pan, Y. F., Note on Schwarz-Pick estimates for bounded and positive real part analytic functions, Proc. Amer. Math. Soc., 136, 2008, 635–640.

    Article  MATH  MathSciNet  Google Scholar 

  6. Frasin, B. A., On analytic functions with positive real part, General Math., 14, 2006, 3–10.

    MATH  MathSciNet  Google Scholar 

  7. Ghatage, P. and Zheng, D. C., Hyperbolic derivatives and generalized Schwarz-Pick estimates, Proc. Amer. Math. Soc., 132, 2004, 3309–3318.

    Article  MATH  MathSciNet  Google Scholar 

  8. Kornyi, A. and Puknszky, L., Holomorphic functions with positive real part on polycylinders, Trans. Amer. Math. Soc., 108, 1963, 449–456.

    Article  MathSciNet  Google Scholar 

  9. Liu, Y. and Chen, Z. H., Schwarz-Pick estimates for positive real part holomorphic functions on unit ball and polydisc, Sci. China Ser. A, 53, 2010. DOI: 10.1007/s11425-009-0197-1

  10. Maccluer, B., Stroethoff, K. and Zhao, R., Generalized Schwarz-Pick estimates, Proc. Amer. Math. Soc., 131, 2002, 593–599.

    Article  MathSciNet  Google Scholar 

  11. Samaris, N., On the extreme points of a subclass of holomorphic functions with positive real part, Math. Ann., 274, 1986, 609–612.

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

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

    Yang Liu

  2. Department of Mathematics, Tongji University, Shanghai, 200092, China

    Zhihua Chen

Authors
  1. Yang Liu
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Zhihua Chen
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Yang Liu.

Additional information

Project supported by the National Natural Science Foundation of China (Nos. 10871145, 10926066) and the Doctoral Program Foundation of the Ministry of Education of China (No. 20090072110053).

Rights and permissions

Reprints and permissions

About this article

Cite this article

Liu, Y., Chen, Z. A note on Schwarz-Pick estimate. Chin. Ann. Math. Ser. B 31, 343–346 (2010). https://doi.org/10.1007/s11401-009-0069-6

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11401-009-0069-6

Keywords

2000 MR Subject Classification

Search

Navigation