Europe/Lisbon
Room P3.10, Mathematics Building Instituto Superior Técnicohttps://tecnico.ulisboa.pt

Nuno J. Alves
Nuno J. Alves, University of Vienna

In this talk, we introduce a parametric bilinear fractional integral operator and obtain uniform bounds via Marcinkiewicz interpolation. This operator is motivated by a reformulation of Euler-Riesz systems, where the nonlocal term in the momentum equation is expressed as the divergence of a tensorial integral operator. This reformulation is relevant as it leads to an a priori higher integrability estimate for the density of finite-energy solutions. The uniform bounds obtained for the parametric fractional integrals then yield bounds for the tensorial integral operator. This is based on joint work with L. Grafakos and A. E. Tzavaras.