Improved Moser-Trudinger-Onofri inequality under constraints

Abstract

A classical result of Aubin states that the constant in Moser-Trudinger-Onofri inequality on ${\mathbb{S}}^2$ can be imporved for furnctions with zero first order moments of the area element. We generalize it to higher order moments case. These new inequalities bear similarity to a sequence of Lebedev-Milin type inequalities on ${\mathbb{S}}^1$ 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.

New references added, to appear in Comm Pure Appl Math

References in corpus (2)

• The sphere covering inequality and its dual
• A remark on the concentration compactness principle in critical dimension