Journal of Inequalities and Applications
Volume 1 (1997), Issue 4, Pages 345-356
Goluzin’s extension of the Schwarz-Pick inequality
Department of Mathematics, Tokyo Metropolitan University Minami-Osawa, Hachioji, Tokyo 192-03, Japan
Received 23 December 1996
Copyright © 1997 Shinji Yamashita. 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.
For a function holomorphic and bounded, , with the expansion
in the disk , we set
Goluzin’s extension of the Schwarz-Pick inequality is that
We shall further improve Goluzin’s inequality with a complete description on the equality
condition. For a holomorphic map from a hyperbolic plane domain into another, one can prove
a similar result in terms of the Poincaré metric.