Stein-Weiss type inequality in L1�1 norm for vector fields and applications.

Tiago Henrique Picon, University of São Paulo, Ribeirão Preto

Abstract: In this talk, we investigate the limit case p = 1 of the Stein–Weiss inequality for the Riesz potential. Our main result is a characterization of this inequality for a special class of vector fields associated to cocanceling operators. As applications, we recovered some classical div-curl inequalities and obtained new solvability results for equations associated to canceling and elliptic differential operators on measures. This is  joint work with Pablo De Nápoli (Universidad de Buenos Aires - Argentina) and Victor Biliatto (UFSCar - Brazil).