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.
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