Bilinear singular integrals and pseudodifferential operators

This work is concerned with the study and use of bilinear Calderón-Zygmund operators and bilinear pseudodifferential operators. We provide a bilinear T1 theorem in the context of Triebel-Lizorkin spaces, which gives sufficient conditions for a bilinear Calderón-Zygmund operator to be bounded on a product of certain such spaces. We also obtain several boundedness results for some classes of bilinear pseudodifferential operators and develop a partial symbolic calculus.; The main tools employed are the atomic decomposition of the Triebel-Lizorkin spaces obtained by Frazier and Jawerth, the bilinear almost diagonal estimates introduced by Grafakos and Torres, the decomposition techniques related to Littlewood-Paley theory and time-frequency analysis developed by Coifman and Meyer, and an extension of the powerful almost orthogonality lemma from the works of Cotlar, and Knapp and Stein, to the multilinear setting.