Compact embeddings of some weighted fractional Sobolev spaces on \Rn

2019/03/21 by Qi Han, Han, Qi
Mathematics · #35S05 #46E35 #Advanced Harmonic Analysis Research #Advanced Mathematical Physics Problems #FOS: Mathematics #Functional Analysis (math.FA) #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.1903.09059

openalex publication_date 2019/03/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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

Related

• Optimal embedding results for fractional Sobolev spaces
• Some necessary and some sufficient conditions for the compactness of the embedding of weighted Sobolev spaces
• Hitchhiker's guide to the fractional Sobolev spaces
• A Compact Embedding Theorem for Generalized Sobolev Spaces
• On compact embeddings in L^p and fractional spaces