On the best constants of Hardy inequality in ${\mathbb{R}}^{n-k}\times ({\mathbb{R}}_{+}{)}^k$ and related improvements

Dan Su, Qiao-Hua Yang

We compute the explicit sharp constants of Hardy inequalities in the cone $\mathbb{R}_{k_+}^{n}:=\mathbb{R}^{n-k}\times (\mathbb{R}_{+})^{k}=\{(x_{1},...,x_{n})|x_{n-k+1}>0,...,x_{…