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arXiv · 2006.05473

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

Ahmed A. Abdelhakim
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Abstract

We prove sharp inequalities of Hardy type for functions in the Sobolev space $W^{1,p}$ on the unit sphere $\mathbb{S}^{n-1}$ in $\mathbb{R}^{n}$. 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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Ahmed A. Abdelhakim. 2020-06-09. Sharp subcritical and critical $L^{p}$ Hardy inequalities on the sphere. https://arxiv.org/abs/2006.05473

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