  We prove the weighted $L^p$ regularity of the ordinary Bergman projection on
certain pseudoconvex domains where the weight belongs to an appropriate
generalization of the B\'{e}koll\`{e}-Bonami class. The main tools used are
estimates on the Bergman kernel obtained by McNeal and B\'{e}koll\`{e}'s
original approach of proving a good-lambda inequality.
