Schwarz-Pick type estimates of pluriharmonic mappings in the unit polydisk
Shaolin Chen, Antti Rasila
TL;DR
This paper extends Schwarz-Pick type estimates to higher-order derivatives of bounded pluriharmonic mappings in the unit polydisk, generalizing classical results from planar harmonic mappings.
Contribution
It provides new estimates for derivatives of pluriharmonic mappings in multiple variables, broadening the scope of classical Schwarz-Pick inequalities.
Findings
Derived higher-order derivative estimates for pluriharmonic mappings
Generalized Colonna's results to multiple variables
Enhanced understanding of pluriharmonic function behavior in polydisks
Abstract
In this paper, we will give Schwarz-Pick type estimates of arbitrary order partial derivatives for bounded pluriharmonic mappings defined in the unit polydisk. Our main results are generalizations of results of Colonna for planar harmonic mappings in [Indiana Univ. Math. J. 38: 829--840, 1989].
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Taxonomy
TopicsAnalytic and geometric function theory · Holomorphic and Operator Theory · Differential Equations and Boundary Problems