Weighted Composition Operators Acting on Harmonic Hardy Spaces

Abstract

Suppose $n\ge 3$ and let $B$ be the open unit ball in ${\mathbb{R}}^n$. Let $\phi :B\to B$ be a $C^2$ map whose Jacobian does not change sign, and let $\psi$ be a $C^2$ function on $B$. We characterize bounded weighted composition operators $W_{\phi ,\psi }$ acting on harmonic Hardy spaces $h^p(B)$. In addition, we compute the operator norm of $W_{\phi ,\psi }$ on $h^p(B)$ when $\phi$ is a Möbius transformation of $B$.