Compactness in quasi-Banach function spaces and applications to compact embeddings of Besov-type spaces
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 Lp (ℝ n ), 1 ⩽ p < ∞, to...
Gespeichert in:
| Veröffentlicht in: | Proceedings of the Royal Society of Edinburgh. Section A. Mathematics 2016-10, Vol.146 (5), p.905-927 |
|---|---|
| Hauptverfasser: | , , |
| Format: | Artikel |
| Sprache: | eng |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| container_end_page | 927 |
|---|---|
| container_issue | 5 |
| container_start_page | 905 |
| container_title | Proceedings of the Royal Society of Edinburgh. Section A. Mathematics |
| container_volume | 146 |
| creator | Caetano, António Gogatishvili, Amiran Opic, Bohumír |
| description | 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 Lp
(ℝ
n
), 1 ⩽ p < ∞, 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 , into Lorentz-type spaces. |
| doi_str_mv | 10.1017/S0308210515000761 |
| format | Article |
| fullrecord | <record><control><sourceid>proquest_cross</sourceid><recordid>TN_cdi_proquest_miscellaneous_1884115908</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><cupid>10_1017_S0308210515000761</cupid><sourcerecordid>4321384661</sourcerecordid><originalsourceid>FETCH-LOGICAL-c485t-792ec916e05bb6d62d00876d23bd69a52682cbbbc5d09c4affba57f4d68a72e63</originalsourceid><addsrcrecordid>eNp1kMtKw0AUhgdRsFYfwN2AGzfROZPMJUtbvIHgQl2HuaVOaWbSTCL07U1oF6K4OnDO9_0cfoQugdwAAXH7RnIiKRAGjBAiOByhGRQizwTQ4hjNpnM23U_RWUrrkeGSiRlaLWPTKtMHlxL2AW8HlXy2UEGZT1wPwfQ-BpxGxCWsgsWqbTfeqGmdcB-x2fvYNdpZ68Mq4VjjhUvxK-t3rTu45-ikVpvkLg5zjj4e7t-XT9nL6-Pz8u4lM4VkfSZK6kwJ3BGmNbecWkKk4Jbm2vJSMcolNVprwywpTaHqWism6sJyqQR1PJ-j631u28Xt4FJfNT4Zt9mo4OKQKpCyAGAlkSN69Qtdx6EL43cTlYMASehIwZ4yXUypc3XVdr5R3a4CUk3VV3-qH5384KhGd96u3I_of61vI_6GFw</addsrcrecordid><sourcetype>Aggregation Database</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype><pqid>1883171802</pqid></control><display><type>article</type><title>Compactness in quasi-Banach function spaces and applications to compact embeddings of Besov-type spaces</title><source>Cambridge University Press Journals Complete</source><creator>Caetano, António ; Gogatishvili, Amiran ; Opic, Bohumír</creator><creatorcontrib>Caetano, António ; Gogatishvili, Amiran ; Opic, Bohumír</creatorcontrib><description>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 Lp
(ℝ
n
), 1 ⩽ p < ∞, 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 , into Lorentz-type spaces.</description><identifier>ISSN: 0308-2105</identifier><identifier>EISSN: 1473-7124</identifier><identifier>DOI: 10.1017/S0308210515000761</identifier><language>eng</language><publisher>Edinburgh, UK: Royal Society of Edinburgh Scotland Foundation</publisher><subject>Criteria ; Function space</subject><ispartof>Proceedings of the Royal Society of Edinburgh. Section A. Mathematics, 2016-10, Vol.146 (5), p.905-927</ispartof><rights>Copyright © Royal Society of Edinburgh 2016</rights><lds50>peer_reviewed</lds50><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c485t-792ec916e05bb6d62d00876d23bd69a52682cbbbc5d09c4affba57f4d68a72e63</citedby></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktohtml>$$Uhttps://www.cambridge.org/core/product/identifier/S0308210515000761/type/journal_article$$EHTML$$P50$$Gcambridge$$H</linktohtml><link.rule.ids>164,314,780,784,27924,27925,55628</link.rule.ids></links><search><creatorcontrib>Caetano, António</creatorcontrib><creatorcontrib>Gogatishvili, Amiran</creatorcontrib><creatorcontrib>Opic, Bohumír</creatorcontrib><title>Compactness in quasi-Banach function spaces and applications to compact embeddings of Besov-type spaces</title><title>Proceedings of the Royal Society of Edinburgh. Section A. Mathematics</title><addtitle>Proceedings of the Royal Society of Edinburgh: Section A Mathematics</addtitle><description>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 Lp
(ℝ
n
), 1 ⩽ p < ∞, 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 , into Lorentz-type spaces.</description><subject>Criteria</subject><subject>Function space</subject><issn>0308-2105</issn><issn>1473-7124</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2016</creationdate><recordtype>article</recordtype><sourceid>ABUWG</sourceid><sourceid>AFKRA</sourceid><sourceid>AZQEC</sourceid><sourceid>BENPR</sourceid><sourceid>CCPQU</sourceid><sourceid>DWQXO</sourceid><sourceid>GNUQQ</sourceid><recordid>eNp1kMtKw0AUhgdRsFYfwN2AGzfROZPMJUtbvIHgQl2HuaVOaWbSTCL07U1oF6K4OnDO9_0cfoQugdwAAXH7RnIiKRAGjBAiOByhGRQizwTQ4hjNpnM23U_RWUrrkeGSiRlaLWPTKtMHlxL2AW8HlXy2UEGZT1wPwfQ-BpxGxCWsgsWqbTfeqGmdcB-x2fvYNdpZ68Mq4VjjhUvxK-t3rTu45-ikVpvkLg5zjj4e7t-XT9nL6-Pz8u4lM4VkfSZK6kwJ3BGmNbecWkKk4Jbm2vJSMcolNVprwywpTaHqWism6sJyqQR1PJ-j631u28Xt4FJfNT4Zt9mo4OKQKpCyAGAlkSN69Qtdx6EL43cTlYMASehIwZ4yXUypc3XVdr5R3a4CUk3VV3-qH5384KhGd96u3I_of61vI_6GFw</recordid><startdate>20161001</startdate><enddate>20161001</enddate><creator>Caetano, António</creator><creator>Gogatishvili, Amiran</creator><creator>Opic, Bohumír</creator><general>Royal Society of Edinburgh Scotland Foundation</general><general>Cambridge University Press</general><scope>AAYXX</scope><scope>CITATION</scope><scope>3V.</scope><scope>7QF</scope><scope>7QQ</scope><scope>7SC</scope><scope>7SE</scope><scope>7SP</scope><scope>7SR</scope><scope>7TA</scope><scope>7TB</scope><scope>7U5</scope><scope>7XB</scope><scope>88I</scope><scope>8AL</scope><scope>8BQ</scope><scope>8FD</scope><scope>8FE</scope><scope>8FG</scope><scope>8FK</scope><scope>ABJCF</scope><scope>ABUWG</scope><scope>AFKRA</scope><scope>ARAPS</scope><scope>AZQEC</scope><scope>BENPR</scope><scope>BGLVJ</scope><scope>CCPQU</scope><scope>DWQXO</scope><scope>F28</scope><scope>FR3</scope><scope>GNUQQ</scope><scope>H8D</scope><scope>H8G</scope><scope>HCIFZ</scope><scope>JG9</scope><scope>JQ2</scope><scope>K7-</scope><scope>KR7</scope><scope>L6V</scope><scope>L7M</scope><scope>L~C</scope><scope>L~D</scope><scope>M0N</scope><scope>M2P</scope><scope>M7S</scope><scope>P5Z</scope><scope>P62</scope><scope>PQEST</scope><scope>PQQKQ</scope><scope>PQUKI</scope><scope>PRINS</scope><scope>PTHSS</scope><scope>Q9U</scope></search><sort><creationdate>20161001</creationdate><title>Compactness in quasi-Banach function spaces and applications to compact embeddings of Besov-type spaces</title><author>Caetano, António ; Gogatishvili, Amiran ; Opic, Bohumír</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c485t-792ec916e05bb6d62d00876d23bd69a52682cbbbc5d09c4affba57f4d68a72e63</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2016</creationdate><topic>Criteria</topic><topic>Function space</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Caetano, António</creatorcontrib><creatorcontrib>Gogatishvili, Amiran</creatorcontrib><creatorcontrib>Opic, Bohumír</creatorcontrib><collection>CrossRef</collection><collection>ProQuest Central (Corporate)</collection><collection>Aluminium Industry Abstracts</collection><collection>Ceramic Abstracts</collection><collection>Computer and Information Systems Abstracts</collection><collection>Corrosion Abstracts</collection><collection>Electronics & Communications Abstracts</collection><collection>Engineered Materials Abstracts</collection><collection>Materials Business File</collection><collection>Mechanical & Transportation Engineering Abstracts</collection><collection>Solid State and Superconductivity Abstracts</collection><collection>ProQuest Central (purchase pre-March 2016)</collection><collection>Science Database (Alumni Edition)</collection><collection>Computing Database (Alumni Edition)</collection><collection>METADEX</collection><collection>Technology Research Database</collection><collection>ProQuest SciTech Collection</collection><collection>ProQuest Technology Collection</collection><collection>ProQuest Central (Alumni) (purchase pre-March 2016)</collection><collection>Materials Science & Engineering Collection</collection><collection>ProQuest Central (Alumni Edition)</collection><collection>ProQuest Central UK/Ireland</collection><collection>Advanced Technologies & Aerospace Collection</collection><collection>ProQuest Central Essentials</collection><collection>ProQuest Central</collection><collection>Technology Collection</collection><collection>ProQuest One Community College</collection><collection>ProQuest Central Korea</collection><collection>ANTE: Abstracts in New Technology & Engineering</collection><collection>Engineering Research Database</collection><collection>ProQuest Central Student</collection><collection>Aerospace Database</collection><collection>Copper Technical Reference Library</collection><collection>SciTech Premium Collection</collection><collection>Materials Research Database</collection><collection>ProQuest Computer Science Collection</collection><collection>Computer Science Database</collection><collection>Civil Engineering Abstracts</collection><collection>ProQuest Engineering Collection</collection><collection>Advanced Technologies Database with Aerospace</collection><collection>Computer and Information Systems Abstracts Academic</collection><collection>Computer and Information Systems Abstracts Professional</collection><collection>Computing Database</collection><collection>Science Database</collection><collection>Engineering Database</collection><collection>Advanced Technologies & Aerospace Database</collection><collection>ProQuest Advanced Technologies & Aerospace Collection</collection><collection>ProQuest One Academic Eastern Edition (DO NOT USE)</collection><collection>ProQuest One Academic</collection><collection>ProQuest One Academic UKI Edition</collection><collection>ProQuest Central China</collection><collection>Engineering Collection</collection><collection>ProQuest Central Basic</collection><jtitle>Proceedings of the Royal Society of Edinburgh. Section A. Mathematics</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Caetano, António</au><au>Gogatishvili, Amiran</au><au>Opic, Bohumír</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Compactness in quasi-Banach function spaces and applications to compact embeddings of Besov-type spaces</atitle><jtitle>Proceedings of the Royal Society of Edinburgh. Section A. Mathematics</jtitle><addtitle>Proceedings of the Royal Society of Edinburgh: Section A Mathematics</addtitle><date>2016-10-01</date><risdate>2016</risdate><volume>146</volume><issue>5</issue><spage>905</spage><epage>927</epage><pages>905-927</pages><issn>0308-2105</issn><eissn>1473-7124</eissn><abstract>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 Lp
(ℝ
n
), 1 ⩽ p < ∞, 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 , into Lorentz-type spaces.</abstract><cop>Edinburgh, UK</cop><pub>Royal Society of Edinburgh Scotland Foundation</pub><doi>10.1017/S0308210515000761</doi><tpages>23</tpages><oa>free_for_read</oa></addata></record> |
| fulltext | fulltext |
| identifier | ISSN: 0308-2105 |
| ispartof | Proceedings of the Royal Society of Edinburgh. Section A. Mathematics, 2016-10, Vol.146 (5), p.905-927 |
| issn | 0308-2105 1473-7124 |
| language | eng |
| recordid | cdi_proquest_miscellaneous_1884115908 |
| source | Cambridge University Press Journals Complete |
| subjects | Criteria Function space |
| title | Compactness in quasi-Banach function spaces and applications to compact embeddings of Besov-type spaces |
| url | https://sfx.bib-bvb.de/sfx_tum?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2024-12-21T07%3A20%3A26IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-proquest_cross&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.genre=article&rft.atitle=Compactness%20in%20quasi-Banach%20function%20spaces%20and%20applications%20to%20compact%20embeddings%20of%20Besov-type%20spaces&rft.jtitle=Proceedings%20of%20the%20Royal%20Society%20of%20Edinburgh.%20Section%20A.%20Mathematics&rft.au=Caetano,%20Ant%C3%B3nio&rft.date=2016-10-01&rft.volume=146&rft.issue=5&rft.spage=905&rft.epage=927&rft.pages=905-927&rft.issn=0308-2105&rft.eissn=1473-7124&rft_id=info:doi/10.1017/S0308210515000761&rft_dat=%3Cproquest_cross%3E4321384661%3C/proquest_cross%3E%3Curl%3E%3C/url%3E&disable_directlink=true&sfx.directlink=off&sfx.report_link=0&rft_id=info:oai/&rft_pqid=1883171802&rft_id=info:pmid/&rft_cupid=10_1017_S0308210515000761&rfr_iscdi=true |