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.
All Science Journal Classification (ASJC) codes
- Applied Mathematics