Sharp subcritical and critical L^p Hardy inequalities on the sphere

2020/06/09 by Abdelhakim, Ahmed A.
#Analysis of PDEs (math.AP) #FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.2006.05473

Abstract

We prove sharp inequalities of Hardy type for functions in the Sobolev space W^1,p on the unit sphere \mathbbS^n-1 in ℝⁿ. We achieve this in both the subcritical and critical cases. The method we use to show optimality takes into account all the constants involved in our inequalities.

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