Let Ω be a bounded strictly pseudoconvex domain in ${ℂ}^n$. In this paper we find sufficient conditions on a function f defined on Ω in order that the weighted Bergman projection $P_{s}f$ belong to the Hardy-Sobolev space $H_k^p\left(\partial \Omega \right)$. The conditions on f we consider are formulated in terms of tent spaces and complex tangential vector fields. If f is holomorphic then these conditions are necessary and sufficient in order that f belong to the Hardy-Sobolev space $H_k^p\left(\partial \Omega \right)$.