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We prove the weighted $L^p$ regularity of the ordinary Bergman andCauchy-Szeg\H{o} projections on strongly pseudoconvex domains $D$ in$\mathbb{C}^n$ with near minimal smoothness for appropriate generalizations ofthe $B_p/A_p$ classes. In particular, the $B_p/A_p$ Muckenhoupt type conditionis expressed relative to balls in a quasi-metric that arises as a space ofhomogeneous type on either the interior or the boundary of the domain $D$.

Weighted $L^p$ Estimates for the Bergman and Szeg\H{o} Projections on Strongly Pseudoconvex Domains with Near Minimal Smoothness