## Kodai Mathematical Journal

### Schwarz-Pick inequalities for convex domains

Jian-Lin Li

#### Abstract

Let Ω and Π be two simply connected domains in the complex plane C, which are not equal to the whole plane C, and let A(Ω, Π) denote the set of functions f : Ω → Π analytic in Ω. Define the quantities Cn (Ω, Π) by

where λΩ and λΠ are the densities of the Poincaré metric in Ω and Π, respectively. We derive sharp upper bounds for |f(n)(z)| (z Ω) and Cn(Ω, Π) if 2 ≤ n ≤ 8 and Ω is a convex domain. The detailed equality condition of the estimate on |f(n)(z)| is also given.

#### Article information

Source
Kodai Math. J., Volume 30, Number 2 (2007), 252-262.

Dates
First available in Project Euclid: 3 July 2007

Permanent link to this document
https://projecteuclid.org/euclid.kmj/1183475516

Digital Object Identifier
doi:10.2996/kmj/1183475516

Mathematical Reviews number (MathSciNet)
MR2343422

Zentralblatt MATH identifier
1134.30016

#### Citation

Li, Jian-Lin. Schwarz-Pick inequalities for convex domains. Kodai Math. J. 30 (2007), no. 2, 252--262. doi:10.2996/kmj/1183475516. https://projecteuclid.org/euclid.kmj/1183475516