Lorentz space estimates for the Coulombian renormalized energy

الأصل · EN

In this paper we obtain optimal estimates for the "currents" associated to point masses in the plane, in terms of the Coulombian renormalized energy of Sandier-Serfaty ss1,ss3. To derive the estimates, we use a technique that we introduced in st, which couples the "ball construction method" to estimates in the Lorentz space L²,∞.