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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 › ‰R2 and on all ofR2. In some cases we also address the question of existence of minimizers. Mathematics Subject Classification. Primary 35J60

Moser-Trudinger and logarithmic HLS inequalities for systems