Some coefficient estimates on real kernel 𝛼-harmonic mappings

Abstract

We call the solution of a kind of second order homogeneous partial differential equation as real kernel α − \alpha - harmonic mappings. For this class of mappings, we explore its Heinz type inequality. Furthermore, for a subclass of real kernel α − \alpha - harmonic mappings with real coefficients, we estimate their coefficients. At last, we study the extremal function of Schwartz type lemma for the class of real kernel α − \alpha - harmonic mappings.

Schwarz Lemma for Solutions of the $$\alpha $$-harmonic Equation

“…Here and hereafter, H k (S n−1 , R n ) denotes the space of spherical harmonic mappings of degree k from S n−1 into R n . For the case when n = 2, we refer to [1,6,9,20,22] for basic properties of the mappings defined in (1.3). For higher dimensional cases, see [17,18,27].…”