Weighted spaces of functions harmonic in the unit ball

We introduce the Banach spaces $h_{\infty}(\varphi)$, $h_{0}(\varphi)$ and $h^{1}(\psi)$ functions harmonic in the unit ball $B\subset\mathbb{R}^n$. These spaces depend on weight functions $\varphi$, $\psi$. We prove that if $\varphi$ and $\psi$ form a normal pair, then $h^{1}(\psi)^*\sim h_{\infty}(\varphi)$ and $h_{0}(\varphi)^*\sim h^{1}(\psi)$.