Boundedness of smooth bilinear square functions and applications to some bilinear pseudo-differential operators

Frederic Bernicot (1) , Saurabh Shrivastava (2)

1 LPP - Laboratoire Paul Painlevé - UMR 8524
2 Department of Mathematics and Statistics [Kanpur]

This paper is devoted to the proof of boundedness of bilinear smooth square functions. Moreover, we deduce boundedness of some bilinear pseudo-differential operators associated with symbols belonging to a subclass of $BS^0_{0,0}$.

Mots clés: Mathematical functions; Integers; Mathematical theorems; Musical intervals; Tiles; Fourier transformations; Reasoning; Mathematical intervals; Mathematical vectors

Domaines: Analyse classique [math.CA]

Frederic Bernicot, Saurabh Shrivastava. Boundedness of smooth bilinear square functions and applications to some bilinear pseudo-differential operators. Indiana University Mathematics Journal, 2011, 60 (1), pp.233-268. ⟨10.1512/iumj.2011.60.4527⟩. ⟨hal-00564541⟩