SHARP HARDY-LITTLEWOOD-SOBOLEV INEQUALITY ON THE UPPER HALF SPACE

By Jingbo Dou, Meijun Zhu. 2013

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There are at least two directions concerning the extension of classical sharp Hardy-Littlewood-Sobolev inequality: (1) Extending the sharp inequality on general manifolds; (2) Extending it for the negative exponent λ = n−α (that is for the case of α > n). In this paper we confirm the possibility for the extension along the first direction by establishing the sharp Hardy-Littlewood-Sobolev inequality on the upper half space (which is conformally equivalent to a ball). The existences of extremal functions are obtained; And for certain range of the exponent, we classify all extremal functions via the method of moving sphere.

Subfields: Applied Mathematics

View Paper: https://www.semanticscholar.org/paper/9e89cd6707f5705eaf5fb954ec5b439e5e91e99f

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In Applied Mathematics

  1. Fengbo Hang
  2. Paul Yang
  3. Yanyan Li
  4. A. Malchiodi
  5. María del Mar González
  6. Wenxiong CHEN *
  7. Congming LI #
  8. C. B. Ndiaye

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