Resumen de Bilinear pseudodifferential operators with symbol in BSm1,1 on Triebel–Lizorkin spaces with critical Sobolev index

Sergio Frias Garcia, Salvador Rodríguez López

• In this paper we obtain new estimates for bilinear pseudodifferential operators with symbol in the class , when both arguments belong to Triebel-Lizorkin spaces of the type . The inequalities are obtained as a consequence of a refinement of the classical Sobolev embedding , where we replace by an appropriate subspace which contains . As an application, we study the product of functions on when , where those spaces fail to be multiplicative algebras.