Bilinear calderón–zygmund operators

Abstract

This chapter is based on the presentation “Generalized bilinear Calderón –Zygmund operators and applications” delivered by the author during the 2008 February Fourier Talks at the Norbert Wiener Center for Harmonic Analysis and Applications, Department of Mathematics, University of Maryland, College Park, on February 21st. In turn, that presentation was based on material from the article “Weighted norm inequalities for paraproducts and bilinear pseudodifferential operators with mild regularity,” J. Fourier Anal. Appl. 15 (2), (2009), 218–261, by Virginia Naibo and the author. This chapter also surveys some more recent results concerning the symbolic calculus and mapping properties of bilinear pseudo-differential operators. The author would like to thank Professor John Benedetto for his inspiration and constant support as well as the organizers of the FFT for their kind invitation and hospitality.