# Some endpoint estimates for bilinear paraproducts and applications

In this talk we will present some endpoint estimates for bilinear paraproducts of Bony’s type. That is, operators of the form $\Pi(f,g)(x)= \int_0^\infty Q_t f(x)\, P_tg(x)\, m(t)\frac{\mathrm{d}t}{t},$ where $P_t$ and $Q_t$ represent frequency localisation operators near the ball $|{\xi}|\lesssim 1/t$ and the annulus $|{\xi}|\thickapprox 1/t$, respectively. More precisely, we will present some new boundedness estimates for bilinear paraproducts operators on local {\rm bmo} spaces.

We will motivate this study by giving some applications to the investigations on the boundedness of bilinear Fourier integral operators and bilinear Coifman-Meyer multipliers.

This is a joint work with W. Staubach (Uppsala University).

This talk is part of the Partial Differential Equations seminar series.