Special Session 114: Recent Advances in Partial Differential Equations and Harmonic Analysis

Stein-Weiss type inequality in L1 norm for vector fields and applications
Tiago Picon
University of Sao Paulo
Brazil
Co-Author(s):    
Abstract:
In this talk, we investigate the endpoint case $p = 1$ of the Stein-Weiss inequality for the Riesz potential. Our main result provides a characterization of this inequality for a special class of complex vector fields associated with cocanceling operators. As an application, we recover and extend several classical inequalities, and we also establish new solvability results for equations involving canceling and elliptic differential operators acting on measures. This work is based on joint research with Jorge Hounie (UFSCar, Brazil), Pablo De Napoli (Universidad de Buenos Aires, Argentina), Victor Biliatto (USP, Brazil), and Joel Coacalle (USP, Brazil)