Compact embeddings of some weighted fractional Sobolev spaces on $\Rn$

Abstract

In this paper, we study a family of general fractional Sobolev spaces $\MsqpOm$ when $\Om=\Rn$ or $\Om$ is a bounded domain, having a compact, Lipschitz boundary $\Bdy$, in $\Rn$ for $n\geq2$. Among other results, some compact embedding results of $\MVsqpRn\hookrightarrow\LqRn$ and $\MVsqpRn\hookrightarrow\LlRn$ for suitable potential functions $V(x)$ are described.