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arXiv · 1708.05225

Weighted Composition Operators Acting on Harmonic Hardy Spaces

Pengyan Hu·Congwen Liu·Taishun Liu·Lifang Zhou
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Abstract

Suppose $n\geq 3$ and let $B$ be the open unit ball in $\mathbb{R}^n$. Let $\varphi: B\to B$ 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 $W_{\varphi,\psi}$ acting on harmonic Hardy spaces $h^p(B)$. In addition, we compute the operator norm of $W_{\varphi,\psi}$ on $h^p(B)$ when $\varphi$ is a M\"obius transformation of $B$.

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Pengyan Hu, Congwen Liu, Taishun Liu, Lifang Zhou. 2017-08-17. Weighted Composition Operators Acting on Harmonic Hardy Spaces. https://arxiv.org/abs/1708.05225

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