Improved Moser-Trudinger-Onofri Inequality under Constraints

Sun Yung A. Chang; Fengbo Hang

doi:10.1002/cpa.21952

Improved Moser-Trudinger-Onofri Inequality under Constraints

Sun Yung A. Chang, Fengbo Hang

Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

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 language	English (US)
Journal	Communications on Pure and Applied Mathematics
DOIs	https://doi.org/10.1002/cpa.21952
State	Accepted/In press - 2020

All Science Journal Classification (ASJC) codes

Mathematics(all)
Applied Mathematics

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10.1002/cpa.21952

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abstract = "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.",

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AB - 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.

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