English

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

Functional Analysis 2020-06-15 v2 Analysis of PDEs

Abstract

We prove sharp inequalities of Hardy type for functions in the Sobolev space W1,pW^{1,p} on the unit sphere Sn1\mathbb{S}^{n-1} in Rn\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.

Keywords

Cite

@article{arxiv.2006.05473,
  title  = {Sharp subcritical and critical $L^{p}$ Hardy inequalities on the sphere},
  author = {Ahmed A. Abdelhakim},
  journal= {arXiv preprint arXiv:2006.05473},
  year   = {2020}
}