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arXiv · 2109.13924

Improved Beckner's inequality for axially symmetric functions on $\mathbb{S}^n$

Changfeng Gui·Yeyao Hu·Weihong Xie
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Abstract

In this article we present various uniqueness and existence results for Q-curvature type equations with a Paneitz operator on $\s^n$ in axially symmetric function spaces. In particular, we show uniqueness results for $n=6, 8$ and improve the best constant of Beckner's inequality in these dimensions for axially symmetric functions under the constraint that their centers of mass are at the origin. As a consequence, the associated first Szeg\"o limit theorem is also proven for axially symmetric functions.

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Changfeng Gui, Yeyao Hu, Weihong Xie. 2021-09-27. Improved Beckner's inequality for axially symmetric functions on $\mathbb{S}^n$. https://arxiv.org/abs/2109.13924

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