On interpolation of cocompact imbeddnings

2010/08/25 by Michael Cwikel, Cwikel, Michael, Kyril Tintarev +1
Mathematics · #46B50 #46B70 #46E35 #Analysis of PDEs (math.AP) #FOS: Mathematics #Functional Analysis (math.FA) #math.AP #math.FA #msc:46B50 #msc:46B70 #msc:46E35

paper · pdf · doi:10.48550/arxiv.1008.4371

This version corrects some minor misprints, includes a more extensive bibliography and survey of related research. No results of the paper have been changed

arxiv created 2011/09/29 · arxiv updated 2011/09/30

Abstract

Cocompactness is a useful weaker counterpart of compactness in the study of imbeddings between function spaces. In this paper we show that subcritical continuous imbeddings of fractional Sobolev spaces and Besov spaces over ℝ^N are cocompact relative to lattice shifts. We use techniques of interpolation spaces to deduce our results from known cocompact imbeddings for classical Sobolev spaces ("vanishing" lemmas of Lieb and Lions). We give examples of applications of cocompactness to compactness of imbeddings of some radial subspaces and to existence of minimizers in some isoperimetric problems.Our research complements a range of previous results, and recalls that there is a natural conceptual framework for unifying them.

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