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

Qi Han

paper

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

arXiv:1903.09059

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 $n \geq 2$ . Among other results, some compact embedding results of $\MVsqpRn\hookrightarrow\LqRn$ and $\MVsqpRn\hookrightarrow\LlRn$ for suitable potential functions $V (x)$ are described.