Analysis Seminar

We will present a sharp criterion for $L^2 \times L^2 \to L^1$ boundedness of bilinear operators associated with multipliers with $L^\infty$ derivatives, given in terms of $L^q$ integrability of the multiplier. More precisely, we will show that boundedness holds if and only if $q<4$. We will then discuss applications of this result concerning bilinear rough singular integrals. This is a joint work with L. Grafakos and D. He.