A Bilinear Pseudodifferential Calculus |
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Authors: | Frédéric Bernicot |
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Institution: | 1.Université Paris-Sud XI,Orsay Cedex,France |
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Abstract: | In this paper we construct a new class of bilinear pseudodifferential operators which contains both the Coifman-Meyer class
as well as the non-translation invariant class closely related both to the bilinear Hilbert transform and previously studied
in Bényi et al. (J. Geom. Anal. 16(3):431–453, 2006), Bényi et al. (J. Anal. Math., 2009), Bernicot (Anal. PDE 1:1–27, 2008) as well as the bilinear Marcinkiewicz class studied in Grafakos and Kalton (Stud. Math. 146(2):115–156, 2001). We prove boundedness on Sobolev spaces for these operators as well as establish a symbolic calculus that exhibits the nice
behavior of our new class under transposition and composition with linear operators. |
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