Resumen de Moser-Trudinger and logarithmic HLS inequalities for systems

Gershon Wolansky, Itai Shafrir

• We prove several optimal Moser-Trudinger and logarithmic Hardy-Littlewood-Sobolev inequalities for systems in two dimensions. These include inequalities on the sphere $S2$, on a bounded domain $\Omega\subset\R2$ and on all of $\R2$. In some cases we also address the question of existence of minimizers.