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

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 Szegö limit theorem is also proven for axially symmetric functions.

arXiv admin note: substantial text overlap with arXiv:2109.13390

References in corpus (1)

• The sphere covering inequality and its dual