2 problems

Let $s\in(-\frac{1}{n},0)$ and let $g:\mathbb{R}^{n}\to\mathbb{R}_{+}$ be an even $s$-concave function such that $0<\int g<+\infty$. Let $\mathcal{L}_{s}$ denote the $s$-polarity o…

Let $s\in(-\frac{1}{n},0)$ and let $g:\mathbb{R}^{n}\to\mathbb{R}_{+}$ be even with $g^{s}\in\mathcal{F}$, where $\mathcal{F}$ is the set of convex lower semicontinuous functions…