Sandrine Grellier

Endpoint for the div-curl lemma in Hardy spaces

We give a div-curl type lemma for the wedge product of closed differential forms on Rn when they have coefficients respectively in a Hardy space and L∞ or BMO. In this latter case, the wedge product belongs to an appropriate Hardy-Orlicz space.

An explicit formula for the cubic Szego equation

We derive an explicit formula for the general solution of the cubic Szego equation and of the evolution equation of the corresponding hierarchy. As an application, we prove that all the solutions corresponding to finite rank Hankel operators are quasiperiodic.

TRUNCATIONS OF MULTILINEAR HANKEL OPERATORS

We extend to multilinear Hankel operators the fact that some truncations of bounded Hankel operators are still bounded. We prove and use a continuity property of bilinear Hilbert transforms on products of Lipschitz spaces and Hardy spaces.