Limit of fractional power Sobolev inequalities

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Abstract

We derive the Moser–Trudinger–Onofri inequalities on the 2-sphere and the 4-sphere as the limiting cases of the fractional power Sobolev inequalities on the same spaces, and justify our approach as the dimensional continuation argument initiated by Thomas P. Branson.

Original languageEnglish (US)
Pages (from-to)1177-1201
Number of pages25
JournalJournal of Functional Analysis
Volume274
Issue number4
DOIs
StatePublished - Feb 15 2018

All Science Journal Classification (ASJC) codes

  • Analysis

Keywords

  • Moser–Trudinger–Onofri inequality
  • Sobolev inequality

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