On properties of solutions to the α-harmonic equation

Peijin Li, Antti Rasila*, Zhi Gang Wang

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

1 Scopus citations

Abstract

The aim of this paper is to establish properties of solutions to the α-harmonic equations: (Formula presented.), where (Formula presented.) is a continuous function and (Formula presented.) denotes the closure of the unit disc (Formula presented.) in the complex plane (Formula presented.). We obtain Schwarz type and Schwarz-Pick type inequalities for solutions to the α-harmonic equation. In particular, for (Formula presented.), solutions to the above equation are called α-harmonic functions. We determine the necessary and sufficient conditions for an analytic function ψ to have the property that (Formula presented.) is α-harmonic function for any α-harmonic function f. Furthermore, we discuss the Bergman-type spaces on α-harmonic functions.

Original languageEnglish
Pages (from-to)1981-1997
Number of pages17
JournalComplex Variables and Elliptic Equations
Volume65
Issue number12
DOIs
StatePublished - 1 Dec 2020

Keywords

  • 35J25
  • Bergman-type spaces
  • Primary 31A05
  • Schwarz lemma
  • Secondary 35C15
  • composition
  • α-harmonic equation
  • α-harmonic function

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