Equivalent Characterizations and Applications of Fractional Sobolev Spaces with Partially Vanishing Traces on $(\hat{I}\mu ,\hat{I}´,D)$-Domains Supporting $D$-Adapted Fractional Hardy Inequalities

Jun Cao, Dachun Yang, Qishun Zhang

Let $\hat{I}\text{c◯}\subset {\mathbb{R}}^n$ be an $(\hat{I}\mu ,\hat{I}´,D)$-domain, with $\hat{I}\mu \in (0,1]$, $\hat{I}´\in (0,\infty ]$, and $D\subset \partial \hat{I}\text{c◯}$ being a closed part of $\partial \hat{I}\text{c◯}$, which is a general open…