Improved Beckner's inequality for axially symmetric functions on Sn
Improved Beckner's inequality for axially symmetric functions on Sn
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DOI：
10.1016/j.jfa.2021.109335
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发表时间：
2021-09
影响因子：
1.7
通讯作者：
C. Gui;Yeyao Hu;Weihong Xie
中科院分区：
文献类型：
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作者：
C. Gui;Yeyao Hu;Weihong Xie
在这篇文章中，我们提出了各种不同的唯一性和存在性结果的Q-曲率型方程的Paneitz算子在Sn轴对称函数空间。特别是，我们证明了唯一性结果n= 6，8和改进的最佳常数Beckner不等式在这些方面的轴对称函数的约束下，他们的质心在原点。作为结果，相关的Szegö型不等式也证明了轴对称函数，这是类似的一系列不等式的第一个从Szegö极限定理。
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 Szegö type inequality is also proven for axially symmetric functions which is similar to the first of a series of inequalities following from the Szegö limit theorem.