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Moser-Trudinger and logarithmic HLS inequalities for systems

Itai Shafrir;  Gershon Wolansky — 2005

Journal of the European Mathematical Society

We prove several optimal Moser–Trudinger and logarithmic Hardy–Littlewood–Sobolev inequalities for systems in two dimensions. These include inequalities on the sphere S 2 , on a bounded domain Ω ⊂ ℝ 2 and on all of ℝ 2 . In some cases we also address the question of existence of minimizers.

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