On the Hörmander classes of bilinear pseudodifferential operators II

Details On the Hörmander classes of bilinear pseudodifferential operators II On the Hörmander classes of bilinear pseudodifferential operators II

2011-12-02

arxiv.org/abs/1112.0486v1

Mathematics

Classical Analysis and ODEs

Scientific paper

Boundedness properties for pseudodifferential operators with symbols in the bilinear H\"ormander classes of sufficiently negative order are proved. The results are obtained in the scale of Lebesgue spaces and, in some cases, end-point estimates involving weak-type spaces and BMO are provided as well. From the Lebesgue space estimates, Sobolev ones are then easily obtained using functional calculus and interpolation. In addition, it is shown that, in contrast with the linear case, operators associated with symbols of order zero may fail to be bounded on products of Lebesgue spaces.

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