Boundedness of the Bergman projection on some weighted mixed norm Lebesgue spaces of the upper-half space

Abstract

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.