Multilinear localization operators

In this paper we introduce a notion of multilinear localization operators. By reinterpreting these operators as multilinear Kohn–Nirenberg pseudodifferential operators, we give sufficient conditions for their boundedness on products of modulation spaces. Moreover, we prove that these conditions are also necessary for the boundedness of the operators. Finally, as application, we construct various examples of bounded multilinear pseudodifferential operators.