  In a recent work, Ionescu and Kenig proved that the Cauchy problem
associatedto the Benjamin-Ono equation is well-posed in $L^2(\mathbb R)$. In
this paper we give a simpler proof of Ionescu and Kenig's result, which
moreover provides stronger uniqueness results. In particular, we prove
unconditional well-posedness in $H^s(\mathbb R)$, for $s>1/4$.
