  In this paper, we prove the boundedness of the Bergman projection on weighted
mixed norm spaces of the upper-half space for some weights that are constructed
using the logarithm function and growth functions. Our necessary and sufficient
condition is the same as in the unweighted case, that is it involves only the
parameters and not the weight. We then provide some applications in terms of
dual and derivative characterization, and an atomic decomposition of the
corresponding Bergman spaces.
