Boundedness of bilinear pseudo-differential operators of $S_{0,0}$-type on $L^2\times L^2$

Abstract

We extend the known result that the bilinear pseudo-differential operators with symbols in the bilinear Hörmander class $B{S}_{0,0}^{-n/2}({\mathbb{R}}^n)$ are bounded from $L^2\times L^2$ to $h^1$. We show that those operators are also bounded from $L^2\times L^2$ to $L^r$ for every $1<r\le 2$. Moreover we give similar results for symbol classes wider than $B{S}_{0,0}^{-n/2}({\mathbb{R}}^n)$. We also give results for symbols of limited smoothness.

31 pages, no figures