The Cauchy problem for the Benjamin-Ono equation in $L^2$ revisited

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 $s>1\mathrm{/}4$.