Sobolev Spaces on Locally Compact Abelian Groups: Compact Embeddings and Local Spaces. (9th February 2014)

• Record Type: Journal Article
• Authors: Górka, Przemysław; Kostrzewa, Tomasz; Reyes, Enrique G.
• Other Names: Zhu Kehe Academic Editor.
• Is Part Of: Journal of function spaces. Volume 2014(2014)
• Publication Date: 2014-02-09
• Subjects: Function spaces -- Periodicals; 515.7305
• DOI: 10.1155/2014/404738
• Languages: English
• ISSNs: 2314-8896

Abstract

Abstract : We continue our research on Sobolev spaces on locally compact abelian (LCA) groups motivated by our work on equations with infinitely many derivatives of interest for string theory and cosmology. In this paper, we focus on compact embedding results and we prove an analog for LCA groups of the classical Rellich lemma and of the Rellich-Kondrachov compactness theorem. Furthermore, we introduce Sobolev spaces on subsets of LCA groups and study its main properties, including the existence of compact embeddings intoL p -spaces.