Abstract
We give higher order derivatives Schwarz-Pick estimates for all positive real part holomorphic functions on B n and D n, and generalize early work on Schwarz-Pick estimate of higher order derivatives for holomorphic functions with positive real part on unit disk in ℂ.
Similar content being viewed by others
References
Anderson J M, Dritschel M A, Rovnyak J. Schwarz-Pick inequalities for the Schur-Agler class on the polydisk and unit ball. ArXiv:math.CV/0702269v1
Boas H P. Majorant series. J Korean Math Soc, 2000, 37: 321–337
Dai S Y, Pan Y F. Note on Schwarz-Pick estimates for bounded and positive real part analytic functions. Proc Amer Math Soc, 2008, 136: 635–640
Edmund L. Darstellung und Begrundung einiger neuerer Ergebnisse der Funktionentheorie, Second edition. Berlin: Springer-Verlag, 1916
Frasin B A. On analytic functions with positive real part. General Math, 2006, 14: 3–10
Ghatage P, Zheng D C. Hyperbolic derivatives and Generalized Schwarz-Pick estimates. Proc Amer Math Soc, 2004, 132: 3309–3318
Korányi A. Pukánszky L. Holomorphic functions with positive real part on polycylinders. Trans Amer Math Soc, 1963, 108: 449–456
Maccluer B, Stroethoff K, Zhao R. Generalized Schwarz-Pick estimates. Proc Amer Math Soc, 2002, 131: 593–599
Narasimhan R. Several Complex Variables. Chicago-London: The University of Chicago Press, 1971
Rudin W. Function Theory in the Unit Ball of ℂn. New York: Springer, 1980
Samaris N. On the extreme points of a subclass of holomorphic functions with positive real part. Math Ann, 1986, 274: 609–612
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Liu, Y., Chen, Z. Schwarz-Pick estimates for positive real part holomorphic functions on unit ball and polydisc. Sci. China Math. 53, 1017–1024 (2010). https://doi.org/10.1007/s11425-009-0205-5
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11425-009-0205-5