A Sharp Inequality on the Exponentiation of Functions on the Sphere

Sun Yung Alice Chang; Changfeng Gui

doi:https://doi.org/10.1002/cpa.22034

A Sharp Inequality on the Exponentiation of Functions on the Sphere

Sun Yung Alice Chang, Changfeng Gui

Mathematics

Princeton University

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

Abstract

In this paper we show a new inequality that generalizes to the unit sphere the Lebedev-Milin inequality of the exponentiation of functions on the unit circle. It may also be regarded as the counterpart on the sphere of the second inequality in the Szegö limit theorem on the Toeplitz determinants on the circle. On the other hand, this inequality is also a variant of several classical inequalities of Moser-Trudinger type on the sphere. The inequality incorporates the deviation of the center of mass from the origin into the optimal inequality of Aubin for functions with mass centered at the origin, and improves Onofri's inequality with the contribution of the shifting of the mass center explicitly expressed.

Original language	American English
Pages (from-to)	1303-1326
Number of pages	24
Journal	Communications on Pure and Applied Mathematics
Volume	76
Issue number	6
DOIs	https://doi.org/10.1002/cpa.22034
State	Published - Jun 2023

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Mathematics(all)
Applied Mathematics

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abstract = "In this paper we show a new inequality that generalizes to the unit sphere the Lebedev-Milin inequality of the exponentiation of functions on the unit circle. It may also be regarded as the counterpart on the sphere of the second inequality in the Szeg{\"o} limit theorem on the Toeplitz determinants on the circle. On the other hand, this inequality is also a variant of several classical inequalities of Moser-Trudinger type on the sphere. The inequality incorporates the deviation of the center of mass from the origin into the optimal inequality of Aubin for functions with mass centered at the origin, and improves Onofri's inequality with the contribution of the shifting of the mass center explicitly expressed.",

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AB - In this paper we show a new inequality that generalizes to the unit sphere the Lebedev-Milin inequality of the exponentiation of functions on the unit circle. It may also be regarded as the counterpart on the sphere of the second inequality in the Szegö limit theorem on the Toeplitz determinants on the circle. On the other hand, this inequality is also a variant of several classical inequalities of Moser-Trudinger type on the sphere. The inequality incorporates the deviation of the center of mass from the origin into the optimal inequality of Aubin for functions with mass centered at the origin, and improves Onofri's inequality with the contribution of the shifting of the mass center explicitly expressed.

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A Sharp Inequality on the Exponentiation of Functions on the Sphere

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