A B\'{e}koll\`{e}-Bonami Class of Weights for Certain Pseudoconvex Domains

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.