Improved Beckner's inequality for axially symmetric functions on S-n

摘要

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 Szego type inequality is also proven for axially symmetric functions which is similar to the first of a series of inequalities following from the Szego limit theorem. (C) 2021 Elsevier Inc. All rights reserved.