Boundedness of bilinear pseudo-differential operators with $BS^m_{0,0}$ symbols on Sobolev spaces

Abstract

In the present paper, bilinear pseudo-differential operators with symbols in the bilinear H\"ormander class $BS^m_{0,0}$ are considered. In particular, the boundedness of these operators on Sobolev spaces is established. Our main result is proved by using symbolic calculus and the boundedness of those operators with certain $S_{0,0}$-type symbols on Lebesgue spaces.