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arXiv · 1909.00431

Improved Moser-Trudinger-Onofri inequality under constraints

Sun-Yung A. Chang·Fengbo Hang
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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.

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Sun-Yung A. Chang, Fengbo Hang. 2019-09-01. Improved Moser-Trudinger-Onofri inequality under constraints. https://arxiv.org/abs/1909.00431

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