A note on Schwarz-Pick lemma for bounded complex-valued harmonic functions in the unit ball of ℝ ⁿ

Abstract

In this paper, the authors prove a Schwarz-Pick lemma for bounded complex-valued harmonic functions in the unit ball of ℝ ⁿ.

Keywords

Harmonic functions / Schwarz-Pick lemma / Unit ball

References

[1] Chen H H. The Schwarz-Pick lemma for planar harmonic mappings. Science China Mathematics, 2011, 54(6): 1101-1118

[2] Ahlfors L V. Conformal Invariants: Topics in Geometric Function Theory, 1973, New York: McGraw-Hill 1-3

[3] Heinz E. On one-to-one harmonic mappings. Pacific J. Math., 1959, 9: 101-105

[4] Axler S, Bourdon P, Wade R. Harmonic Function Theory, 2001 Second Edition New York: Springer-Verlag