论文标题
最佳关键指数$ l^{p} $通过Xiao的方法在球体上的Hardy类型不平等
Optimal critical exponent $L^{p}$ inequalities of Hardy type on the sphere via Xiao's method
论文作者
论文摘要
首先，我们纠正[Abimbola Abolarinwa，Kamilu Rauf，Songting Yin，Sharp $ L^{p} $ hardy类型和不确定性原理不等式，数学不等式杂志，13，4（2019），1011-1022]，并获得$ L^$ l^p}的尖锐版本。 $ \ mathbb {s}^{n} $ for $ 2 \ leq p <n $。其次，我们证明了Sphere $ \ Mathbb {s}^{n} $ in $ \ MATHBB {r}^{r}^{n+1} $，$ n \ geq 2 $中的尖锐关键指数$ l^{n} $不等式。这个问题的奇异性是从球体上的任意点的大地距离距离。
First, we correct the proof presented in [Abimbola Abolarinwa, Kamilu Rauf, Songting Yin, Sharp $L^{p}$ Hardy type and uncertainty principle inequalities on the sphere, Journal of Mathematical Inequalities, 13, 4 (2019), 1011 - 1022] and obtain a correct sharp version of an $L^{p}$ Hardy inequality on the sphere $\mathbb{S}^{n}$ for all $2\leq p<n$. Secondly, we prove sharp critical exponent $L^{n}$ inequalities on the sphere $\mathbb{S}^{n}$ in $\mathbb{R}^{n+1}$, $n\geq 2$. The singularity in this problem is the geodesic distance from an arbitrary point on the sphere.
