Boundedness of multilinear pseudo-differential operators with symbols in the H\"ormander class $S_{0,0}$

The multilinear pseudo-differential operators with symbols in the multilinear H"ormander class $S_{0,0}$ are considered. A complete identification of the cases where those operators define bounded operators between local Hardy spaces is given. Some results for the boundedness between Wiener amalgam spaces are also given. These are extensions and improvements of the results known in the bilinear case.