Limited smoothness conditions with mixed norms for bilinear Fourier multipliers

Abstract

In this paper, the $L^2\times L^{\infty }\to L^2$ and $L^2\times L^2\to L^1$ boundedness of bilinear Fourier multiplier operators is discussed under weak smoothness conditions on multipliers. As an application, we prove the $L^2\times BMO\to L^2$ and $L^2\times L^2\to H^1$ boundedness of bilinear operators with multipliers of limited smoothness satisfying vanishing conditions.

22 pages