The Michigan Mathematical Journal

Some refined Schwarz-Pick lemmas

H. Turgay Kaptanoğlu

Full-text: Open access

Article information

Source
Michigan Math. J., Volume 50, Issue 3 (2002), 649 -664.

Dates
First available in Project Euclid: 4 December 2002

Permanent link to this document
https://projecteuclid.org/euclid.mmj/1039029986

Digital Object Identifier
doi:10.1307/mmj/1039029986

Mathematical Reviews number (MathSciNet)
MR2798

Zentralblatt MATH identifier
1026.32023

Subjects
Primary: 32F45: Invariant metrics and pseudodistances 30F45: Conformal metrics (hyperbolic, Poincaré, distance functions) 30C80: Maximum principle; Schwarz's lemma, Lindelöf principle, analogues and generalizations; subordination
Secondary: 51M09: Elementary problems in hyperbolic and elliptic geometries

Citation

Kaptanoğlu, H. Turgay. Some refined Schwarz-Pick lemmas. Michigan Math. J. 50 (2002), no. 3, 649 --664. doi:10.1307/mmj/1039029986. https://projecteuclid.org/euclid.mmj/1039029986


Export citation

References

  • A. F. Beardon, The Schwarz--Pick lemma for derivatives, Proc. Amer. Math. Soc. 125 (1997), 3255--3256.
  • A. F. Beardon and T. K. Carne, A strengthening of the Schwarz--Pick inequality, Amer. Math. Monthly 99 (1992), 216--217.
  • D. M. Burns and S. G. Krantz, Rigidity of holomorphic mappings and a new Schwarz lemma at the boundary, J. Amer. Math. Soc. 7 (1994), 661--676.
  • C. C. Cowen and B. D. MacCluer, Composition operators on spaces of analytic functions, Stud. Adv. Math., CRC Press, Boca Raton, FL, 1995.
  • P. L. Duren, Univalent functions, Grundlehren Math. Wiss., 259, Springer, New York, 1983.
  • J. B. Garnett, Bounded analytic functions, Pure Appl. Math., 96, Academic Press, New York, 1981.
  • P. R. Mercer, Sharpened versions of the Schwarz lemma, J. Math. Anal. Appl. 205 (1997), 509--511.
  • R. Osserman, A new variant of the Schwarz--Pick--Ahlfors lemma, Manuscripta Math. 100 (1999), 123--129.
  • ------, A sharp Schwarz inequality on the boundary, Proc. Amer. Math. Soc. 128 (2000), 3513--3517.
  • W. Rudin, Function theory in the unit ball of $\Bbb C^n,$ Grundlehren Math. Wiss., 241, Springer, New York, 1980.