5 problems

Let $s\in(0,1)$ and let $n$ satisfy … so that $n\leq 3$. Let $\lambda$ be the parameter in the best constant $\mathcal S_s^{\lambda,{2^*_s}}(\mathbb R^n_+)$, and let…

Sharp fractional Poincaré bound conjecture. The correct dependence of the bound on $\delta$ is

Let $\lambda_1$ denote the first relevant eigenvalue arising in the linearized problem for the fractional Caffarelli–Kohn–Nirenberg inequality, and let the parameter space consist…

Let $s\in(0,1)$, let $n$ be the dimension, let $\lambda$ be in the range considered for $\mathcal S_s^{\lambda,{2^*_s}}(\mathbb R^n_+)$, and let…

Let $D$ be a domain in ${\mathbb R^d}$, let $\alpha\in(1,2)$, and let $\Omega\subset D$ be an open convex set. Define $\kappa(\Omega)$ to be the largest number such that … for ever…