Title: Wavelets and Bilinear Operators
Abstract: We use compactly supported wavelets due to Daubechies to prove the strong boundedness of the bilinear singular integral operator
$$T(f,g)(x)=p.v. \int_{\mathbb R^{2n}}\frac{\Omega ((y,z)/|(y,z)|)}{|(y,z)|^{2n}}f(x-y)g(x-z)dydz,$$
where $\Omega\in L^{\infty}(\mathbb S^{2n-1})$ has the vanishing integral.
Using these wavelets, we show also the boundedness of the bilinear operators defined by the Hörmander type multipliers, which are locally in the Sobolev spaces $W^{r,s}(\mathbb R^{2n})$ with $r>4$ and $s>n/2$. The condition $s\ge n/2$ is also necessary.
Joint work with Loukas Grafakos and Petr Honzík.