Duality in spaces of functions pluriharmonic in the unit ball in $\mathbb{C}^n$

Banach spaces $h_\infty (\varPhi)$, $h_0 (\varPhi)$ and $h^1(\eta) $ of functions, pluriharmonic in the unit ball in $\mathbb{C}^n$, depending on weight function $\varPhi$ and weighting measure $\eta$ are introduced. The question we consider is: for given $\varPhi$ we find a finite positive Borel measure $\eta$ on $[0,1)$ such that $h^1(\eta)^* $ $\thicksim$ $h_\infty (\varPhi)$ and $h_0 (\varPhi)^*$ $\thicksim$ $h^1(\eta)$.