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Multilinear pseudodifferential operators beyond Calderón-Zygmund theory. (English) Zbl 1348.47038

Summary: 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 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 Hörmander \(S_{\rho,\delta}^m\) classes. These results are new in the case \(\rho<1\), that is, outwith the scope of multilinear Calderón-Zygmund theory.

MSC:

47G30 Pseudodifferential operators
42B20 Singular and oscillatory integrals (Calderón-Zygmund, etc.)
35J65 Nonlinear boundary value problems for linear elliptic equations
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