{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,1]],"date-time":"2026-04-01T14:38:47Z","timestamp":1775054327787,"version":"3.50.1"},"reference-count":0,"publisher":"European Mathematical Society - EMS - Publishing House GmbH","issue":"1","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Z. Anal. Anwend."],"published-print":{"date-parts":[[2011,1,3]]},"abstract":"<jats:p>\n                    We present conditions which are necessary and sufficient for compact embeddings of Bessel potential spaces\n                    <jats:inline-formula>\n                      <jats:tex-math>H^\\sigma X(\\mathbb R^n)<\/jats:tex-math>\n                    <\/jats:inline-formula>\n                    , modelled upon a rearrangement-invariant Banach function spaces\n                    <jats:inline-formula>\n                      <jats:tex-math>X(\\mathbb R^n)<\/jats:tex-math>\n                    <\/jats:inline-formula>\n                    , into generalized H\u00f6lder spaces involving\n                    <jats:italic>k<\/jats:italic>\n                    -modulus of smoothness. To this end, we derive a characterization of compact subsets of generalized H\u00f6lder spaces. We apply our results to the case when\n                    <jats:inline-formula>\n                      <jats:tex-math>X(\\mathbb R^n)<\/jats:tex-math>\n                    <\/jats:inline-formula>\n                    is a Lorentz\u2013Karamata space\n                    <jats:inline-formula>\n                      <jats:tex-math>L_{p,q;b}(\\mathbb R^n)<\/jats:tex-math>\n                    <\/jats:inline-formula>\n                    . Applications cover both superlimiting and limiting cases.\n                  <\/jats:p>","DOI":"10.4171\/zaa\/1421","type":"journal-article","created":{"date-parts":[[2011,1,3]],"date-time":"2011-01-03T17:45:18Z","timestamp":1294076718000},"page":"1-27","source":"Crossref","is-referenced-by-count":6,"title":["Compact Embeddings of Bessel-Potential-Type Spaces into Generalized H\u00f6lder Spaces Involving $k$-Modulus of Smoothness"],"prefix":"10.4171","volume":"30","author":[{"given":"Amiran","family":"Gogatishvili","sequence":"first","affiliation":[{"name":"Czech Academy of Sciences, Prague, Czech Republic"}]},{"given":"J\u00falio S.","family":"Neves","sequence":"additional","affiliation":[{"name":"Universidade de Coimbra, Portugal"}]},{"given":"Bohum\u00edr","family":"Opic","sequence":"additional","affiliation":[{"name":"Czech Academy of Sciences, Prague, Czech Republic"}]}],"member":"2673","container-title":["Zeitschrift f\u00fcr Analysis und ihre Anwendungen"],"original-title":[],"link":[{"URL":"http:\/\/www.ems-ph.org\/fulltext\/10.4171\/ZAA\/1421","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,11,12]],"date-time":"2025-11-12T14:03:24Z","timestamp":1762956204000},"score":1,"resource":{"primary":{"URL":"https:\/\/ems.press\/doi\/10.4171\/zaa\/1421"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2011,1,3]]},"references-count":0,"journal-issue":{"issue":"1"},"URL":"https:\/\/doi.org\/10.4171\/zaa\/1421","relation":{},"ISSN":["0232-2064","1661-4534"],"issn-type":[{"value":"0232-2064","type":"print"},{"value":"1661-4534","type":"electronic"}],"subject":[],"published":{"date-parts":[[2011,1,3]]}}}