On the boundedness of certain bilinear oscillatory integral operators

Abstract

We prove the global L 2 × L 2 → L 1 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.