{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,10]],"date-time":"2026-03-10T11:33:22Z","timestamp":1773142402570,"version":"3.50.1"},"reference-count":0,"publisher":"Cambridge University Press (CUP)","issue":"5","license":[{"start":{"date-parts":[[2016,6,23]],"date-time":"2016-06-23T00:00:00Z","timestamp":1466640000000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Proceedings of the Royal Society of Edinburgh: Section A Mathematics"],"published-print":{"date-parts":[[2016,10]]},"abstract":"<jats:p>There are two main aims of the paper. The first is to extend the criterion for the precompactness of sets in Banach function spaces to the setting of quasi-Banach function spaces. The second is to extend the criterion for the precompactness of sets in the Lebesgue spaces <jats:italic>L<jats:sub>p<\/jats:sub><\/jats:italic>(\u211d<jats:italic><jats:sup>n<\/jats:sup><\/jats:italic>), 1 \u2a7d <jats:italic>p<\/jats:italic> &lt; \u221e, to the so-called power quasi-Banach function spaces. These criteria are applied to establish compact embeddings of abstract Besov spaces into quasi-Banach function spaces. The results are illustrated on embeddings of Besov spaces <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"gif\" xlink:type=\"simple\" xlink:href=\"S0308210515000761_inline02\"\/>, into Lorentz-type spaces.<\/jats:p>","DOI":"10.1017\/s0308210515000761","type":"journal-article","created":{"date-parts":[[2016,6,23]],"date-time":"2016-06-23T10:29:41Z","timestamp":1466677781000},"page":"905-927","source":"Crossref","is-referenced-by-count":14,"title":["Compactness in quasi-Banach function spaces and applications to compact embeddings of Besov-type spaces"],"prefix":"10.1017","volume":"146","author":[{"given":"Ant\u00f3nio","family":"Caetano","sequence":"first","affiliation":[]},{"given":"Amiran","family":"Gogatishvili","sequence":"additional","affiliation":[]},{"given":"Bohum\u00edr","family":"Opic","sequence":"additional","affiliation":[]}],"member":"56","published-online":{"date-parts":[[2016,6,23]]},"container-title":["Proceedings of the Royal Society of Edinburgh: Section A Mathematics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0308210515000761","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,4,18]],"date-time":"2019-04-18T22:13:41Z","timestamp":1555625621000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0308210515000761\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2016,6,23]]},"references-count":0,"journal-issue":{"issue":"5","published-print":{"date-parts":[[2016,10]]}},"alternative-id":["S0308210515000761"],"URL":"https:\/\/doi.org\/10.1017\/s0308210515000761","relation":{},"ISSN":["0308-2105","1473-7124"],"issn-type":[{"value":"0308-2105","type":"print"},{"value":"1473-7124","type":"electronic"}],"subject":[],"published":{"date-parts":[[2016,6,23]]}}}