  Consider a bounded, strongly pseudoconvex domain $D\subset \mathbb C^n$ with
minimal smoothness (namely, the class $C^2$) and let $b$ be a locally
integrable function on $D$. We characterize boundedness (resp., compactness) in
$L^p(D), p > 1$, of the commutator $[b, P]$ of the Bergman projection $P$ in
terms of an appropriate bounded (resp. vanishing) mean oscillation requirement
on $b$. We also establish the equivalence of such notion of BMO (resp., VMO)
with other BMO and VMO spaces given in the literature. Our proofs use a dyadic
analog of the Berezin transform and holomorphic integral representations going
back (for smooth domains) to N. Kerzman & E. M. Stein, and E. Ligocka.
