On the boundedness of certain bilinear oscillatory integral operators

Rodríguez-López, Salvador; Rule, David; Staubach, Wolfgang

doi:10.1090/S0002-9947-2015-06244-8

On the boundedness of certain bilinear oscillatory integral operators
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by Salvador Rodríguez-López, David Rule and Wolfgang Staubach PDF

Trans. Amer. Math. Soc. 367 (2015), 6971-6995 Request permission

Abstract:

We prove the global $L^2 \times L^2 \to L^1$ boundedness of bilinear oscillatory integral operators with amplitudes satisfying a Hörmander-type condition and phases satisfying appropriate growth as well as the strong non-degeneracy conditions. This is an extension of the corresponding result of R. Coifman and Y. Meyer for bilinear pseudodifferential operators, to the case of oscillatory integral operators.

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