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

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