On properties of the solutions to the (p,q)-harmonic functions

Abstract

Suppose $p,q\in R﹨Z^{-}$ such that $p+q>-1$. The aim of this paper is to establish properties of the $(p,q)$-harmonic functions in the unit disc $\left|z\right|<1$ in the complex plane $C$. We obtain the boundedness and the Lipschitz continuity with respect to the hyperbolic metric for $(p,q)$-harmonic functions. In particular, for $p=q>-1$, we get the Heinz type inequality on the unit circle $\left|z\right|=1$. As an application, a Landau type theorem of $(p,q)$-harmonic functions is established.