Sobolev Spaces on Locally Compact Abelian Groups: Compact Embeddings and Local Spaces
Copyright policy )Sobolev Spaces on Locally Compact Abelian Groups: Compact Embeddings and Local Spaces
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 intoLp-spaces.
compact embedding, QA1-939, Sobolev spaces and other spaces of ``smooth'' functions, embedding theorems, trace theorems, Sobolev spaces on locally compact abelian groups, Mathematics
compact embedding, QA1-939, Sobolev spaces and other spaces of ``smooth'' functions, embedding theorems, trace theorems, Sobolev spaces on locally compact abelian groups, Mathematics
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