Multilinear pseudodifferential operators beyond Calder\'on-Zygmund theory

Abstract

We consider two types of multilinear pseudodifferential operators. First, we prove the boundedness of multilinear pseudodifferential operators with symbols which are only measurable in the spatial variables in weighted Lebesgue spaces. These results generalise earlier work of the present authors concerning linear pseudo-pseudodifferential operators. Secondly, we investigate the boundedness of bilinear pseudodifferential operators with symbols in the H\"ormander $S^{m}_{\rho, \delta}$ classes. These results are new in the case $\rho < 1$, that is, outwith the scope of multilinear Calder\'on-Zygmund theory.