The paper says that since $u = - \nabla \times (\Delta^{-1} \omega)$ "The Fourier transforms of $\nabla u$ and $\omega$ satisfy $(\nabla u)^{\text{^}}(\xi) = S(\xi)\hat\omega(\xi)$ where $S$ is a matrix which is bounded independent of $\xi$".
Does anyone recognize this theorem? Where could I find a proof for it?
Thanks for any light into this.
As for the meaning of $\Delta^{-1} \omega$, I think it is to choose some $f$ satisfying $\Delta f = \omega$ (even though this is not unique). Further it is a correction of the typo to write $\Delta$ instead of $\nabla$ as they did in the paper.