naa a22 4500 510760686 CHVBK 20180411083138.0 cr unu---uuuuu 180411e20130101xx s 000 0 eng 10.1007/s13163-011-0087-2 doi (NATIONALLICENCE)springer-10.1007/s13163-011-0087-2 On interpolation of cocompact imbeddings [Elektronische Daten] [Michael Cwikel, Kyril Tintarev] Cocompactness is a useful weaker counterpart of compactness in the study of imbeddings between function spaces. In this paper we prove that, under quite general conditions, cocompactness of imbeddings of Banach spaces persists under both real and complex interpolation. As an application, we obtain that subcritical continuous imbeddings of fractional Sobolev spaces and Besov spaces are cocompact relative to lattice shifts. We deduce this by interpolating the known cocompact imbeddings for classical Sobolev spaces ("vanishing” lemmas of Lieb and Lions). We also apply cocompactness to prove compactness of imbeddings of some radial subspaces and to show the 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. The Author(s), 2011 Besov spaces nationallicence Cocompact imbeddings nationallicence Concentration compactness nationallicence Fractional Sobolev spaces nationallicence Interpolation spaces nationallicence Minimizers nationallicence Mollifiers nationallicence Sobolev imbeddings nationallicence Cwikel Michael Department of Mathematics, Technion-Israel Institute of Technology, 32000, Haifa, Israel aut Tintarev Kyril Department of Mathematics, Uppsala University, P.O. Box 480, 75 106, Uppsala, Sweden aut Revista Matemática Complutense Springer Milan 26/1(2013-01-01), 33-55 1139-1138 26:1<33 2013 26 13163 https://doi.org/10.1007/s13163-011-0087-2 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s13163-011-0087-2 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Cwikel Michael Department of Mathematics, Technion-Israel Institute of Technology, 32000, Haifa, Israel aut NATIONALLICENCE 700 1- Tintarev Kyril Department of Mathematics, Uppsala University, P.O. Box 480, 75 106, Uppsala, Sweden aut NATIONALLICENCE 773 0- Revista Matemática Complutense Springer Milan 26/1(2013-01-01), 33-55 1139-1138 26:1<33 2013 26 13163 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer