A $({\varphi }_{\frac{n}{s}},\varphi )$-Poincaré inequality in John domain

Shangying Feng, Tian Liang

Let $\Omega$ be a bounded domain in ${\mathbb{R}}^n$ with $n\ge 2$ and $s\in (0,1)$. Assume that $\varphi :[0,\infty )\to [0,\infty )$ be a Young function obeying the doubling condition with the…