Improved Moser-Trudinger-Onofri Inequality under Constraints

Sun Yung A. Chang, Fengbo Hang

Research output: Contribution to journalArticlepeer-review


A classical result of Aubin states that the constant in the Moser-Trudinger-Onofri inequality on (Formula presented.) can be improved for functions with zero first-order moments of the area element. We generalize it to the higher-order moments case. These new inequalities bear similarity to a sequence of Lebedev-Milin-type inequalities on (Formula presented.) coming from the work of Grenander-Szego on Toeplitz determinants (as pointed out by Widom). We also discuss the related sharp inequality by a perturbation method.

Original languageEnglish (US)
Pages (from-to)197-220
Number of pages24
JournalCommunications on Pure and Applied Mathematics
Issue number1
StatePublished - Jan 2022

ASJC Scopus subject areas

  • General Mathematics
  • Applied Mathematics


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