Boundedness of bilinear pseudo-differential operators of $S_{0,0}$-type in Wiener amalgam spaces and in Lebesgue spaces

Abstract

We extend and improve the known results about the boundedness of the bilinear pseudo-differential operators with symbols in the bilinear H\"ormander class $BS^{m}_{0,0}(\mathbb{R}^n)$. We consider wider classes of symbols and improve estimates for the corresponding operators. A key idea is to consider the operators in Wiener amalgam spaces.