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Sobolev continuity of certain paradifferential operators. (Continuité-Sobolev de certains opérateurs paradifférentiels.) (French) Zbl 0776.47024

The aim of this paper is to characterize the boundedness of certain paradifferential operators on Besov spaces \(\dot B^ s_{p,q}\). These paradifferential operators arise naturally in the extension of the \(T(1)\)-theorem for singular integral operators to Sobolev spaces \(\dot H^ s\), \(s>0\).

MSC:

47G30 Pseudodifferential operators
46E35 Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems
35S50 Paradifferential operators as generalizations of partial differential operators in context of PDEs
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