Multilinear Localization Operators
نویسندگان
چکیده
In this paper we introduce a notion of multilinear localization operators. By reinterpreting these operators as multilinear Kohn-Nirenberg pseudodifferential operators, we prove that these multilinear localization operators are bounded on products of modulation spaces. In particular, by assuming that the symbols of the localization operators belong to the largest modulation space, i.e., M , we show that the symbols of the corresponding pseudodifferential operators belong to the modulation space M. The boundedness properties of the localization operators, then follow from known results on boundedness of multilinear pseudodifferential operators on products of modulation spaces. Moreover, we show the sufficient boundedness condition is also necessary. Finally, as application we construct various examples of bounded multilinear pseudodifferential operators with symbols in M.
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