We study the duals of the spaces $A^{pα}(X)$ of harmonic functions in the unit ball of $ℝ^n$ with values in a Banach space X, belonging to the Bochner $L^p$ space with weight $(1-|x|)^α$, denoted by $L^{pα}(X)$. For 0 < α < p-1 we construct continuous pro