JournalsjemsVol. 7, No. 4pp. 413–448

Moser-Trudinger and logarithmic HLS inequalities for systems

  • Itai Shafrir

    Technion - Israel Institute of Technology, Haifa, Israel
  • Gershon Wolansky

    Technion - Israel Institute of Technology, Haifa, Israel
Moser-Trudinger and logarithmic HLS inequalities for systems cover
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Abstract

We prove several optimal Moser-Trudinger and logarithmic Hardy-Littlewood-Sobolev inequalities for systems in two dimensions. These include inequalities on the sphere S2S2, on a bounded domain ΩR2\Omega\subset\R2 and on all of R2\R2. In some cases we also address the question of existence of minimizers.

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Itai Shafrir, Gershon Wolansky, Moser-Trudinger and logarithmic HLS inequalities for systems. J. Eur. Math. Soc. 7 (2005), no. 4, pp. 413–448

DOI 10.4171/JEMS/34