On the setting of the upper half-space H of the Eu­clidean n-space, we show the boundedness of weighted Bergman projection for 1 < p < $infty$ and nonorthogonal projections for 1 $leq$ p < $infty$ . Using these results, we show that Bergman norm is equiva­ lent to the normal derivative norms on weighted harmonic Bergman spaces. Finally, we find the dual of b$\_{$^{1}$.