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arXiv · 1711.00724

Limiting case Hardy inequalities on the sphere

Ahmed A. Abdelhakim
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Abstract

We give sharp limiting case Hardy inequalities on the sphere $\mathbb{S}^{2}$ and show that their optimal constants are unattainable by any $f\in H^{1}\left(\mathbb{S}^{2}\right)\setminus\{0\}$. The singularity of the problem is related to the geodesic distance from a point on the sphere.

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Ahmed A. Abdelhakim. 2017-11-02. Limiting case Hardy inequalities on the sphere. https://arxiv.org/abs/1711.00724

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