English

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

Functional Analysis 2019-03-22 v1

Abstract

In this paper, we study a family of general fractional Sobolev spaces \MsqpOm\MsqpOm when \Om=\Rn\Om=\Rn or \Om\Om is a bounded domain, having a compact, Lipschitz boundary \Bdy\Bdy, in \Rn\Rn for n2n\geq2. Among other results, some compact embedding results of \MVsqpRn\LqRn\MVsqpRn\hookrightarrow\LqRn and \MVsqpRn\LlRn\MVsqpRn\hookrightarrow\LlRn for suitable potential functions V(x)V(x) are described.

Keywords

Cite

@article{arxiv.1903.09059,
  title  = {Compact embeddings of some weighted fractional Sobolev spaces on $\Rn$},
  author = {Qi Han},
  journal= {arXiv preprint arXiv:1903.09059},
  year   = {2019}
}