On Sharp Beckner's Inequality for Axially Symmetric Functions on \mathbbS⁴

2022/12/08 by Tuoxin Li, Juncheng Wei, Li, Tuoxin +3
Mathematics · #Analysis of PDEs (math.AP) #Analytic and geometric function theory #Differential Geometry (math.DG) #FOS: Mathematics #Mathematical functions and polynomials #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.2212.04099

openalex publication_date 2022/12/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove a sharp Beckner's inequality for axially symmetric functions on S⁴. The key ingredients of our proof is some pointwise quantitative properties of Gegenbauer polynomials.

Related

• Improved Beckner's inequality for axially symmetric functions on \mathbbSⁿ
• Improved Beckner's inequality for axially symmetric functions on \mathbbS⁴
• On Beckner's Inequality for Axially Symmetric Functions on \mathbbS⁶
• A sharp symmetric integral form of the John-Nirenberg inequality
• On the Stein-Weiss inequalities and higher-order Caffarelli-Kohn-Nirenberg type inequalities: sharp constants, symmetry of extremal functions