The Bohr radius of the unit ball of
Identifieur interne : 001A73 ( Istex/Corpus ); précédent : 001A72; suivant : 001A74The Bohr radius of the unit ball of
Auteurs : Andreas Defant ; Leonhard FrerickSource :
- Journal für die reine und angewandte Mathematik (Crelles Journal) [ 0075-4102 ] ; 2011-11.
Abstract
By a classical result due to Aizenberg, Boas and Khavinson the Bohr radius of the unit ball in the Minkowski space , 1 ≦ p ≦ ∞, is up to an absolute constant ≦ (log n/n)1–1/min(p, 2). Our main result shows that this estimate is optimal. For p = ∞, this was recently proved in [Defant, Frerick, Ortega-Cerdà, Ounaies and Seip, Ann. Math. 174: 1–13, 2011] as a consequence of the hypercontractivity of the Bohnenblust–Hille inequality for polynomials. Using substantially different methods from local Banach space theory, we give a proof which covers the full scale 1 ≦ p ≦ ∞.
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DOI: 10.1515/crelle.2011.080
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For p = ∞, this was recently proved in [Defant, Frerick, Ortega-Cerdà, Ounaies and Seip, Ann. Math. 174: 1–13, 2011] as a consequence of the hypercontractivity of the Bohnenblust–Hille inequality for polynomials. Using substantially different methods from local Banach space theory, we give a proof which covers the full scale 1 ≦ p ≦ ∞.</div></front></TEI><istex><corpusName>degruyter-journals</corpusName><author><json:item><name>Andreas Defant</name><affiliations><json:string>Institut of Mathematics, Carl von Ossietzky Universität, 26111, Oldenburg, Germany</json:string></affiliations></json:item><json:item><name>Leonhard Frerick</name><affiliations><json:string>Fachbereich IV - Mathematik, Universität Trier, 54294, Trier, Germany</json:string></affiliations></json:item></author><articleId><json:string>crll.2011.660.131</json:string></articleId><language><json:string>eng</json:string></language><originalGenre><json:string>research-article</json:string></originalGenre><abstract>By a classical result due to Aizenberg, Boas and Khavinson the Bohr radius of the unit ball in the Minkowski space , 1 ≦ p ≦ ∞, is up to an absolute constant ≦ (log n/n)1–1/min(p, 2). Our main result shows that this estimate is optimal. For p = ∞, this was recently proved in [Defant, Frerick, Ortega-Cerdà, Ounaies and Seip, Ann. Math. 174: 1–13, 2011] as a consequence of the hypercontractivity of the Bohnenblust–Hille inequality for polynomials. Using substantially different methods from local Banach space theory, we give a proof which covers the full scale 1 ≦ p ≦ ∞.</abstract><qualityIndicators><score>8.212</score><pdfVersion>1.4</pdfVersion><pdfPageSize>539 x 737 pts</pdfPageSize><refBibsNative>false</refBibsNative><keywordCount>0</keywordCount><abstractCharCount>574</abstractCharCount><pdfWordCount>5719</pdfWordCount><pdfCharCount>23974</pdfCharCount><pdfPageCount>17</pdfPageCount><abstractWordCount>101</abstractWordCount></qualityIndicators><title>The Bohr radius of the unit ball of</title><refBibs><json:item><author><json:item><name>L Aizenberg</name></json:item></author><host><volume>128</volume><pages><last>1155</last><first>1147</first></pages><issue>4</issue><author></author><title>Proc. Amer. Math. 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KG</publisher><availability><p>© Walter de Gruyter Berlin · New York 2011, 2011</p></availability><date>2011-06-28</date></publicationStmt><sourceDesc><biblStruct type="inbook"><analytic><title level="a" type="main" xml:lang="en">The Bohr radius of the unit ball of</title><author xml:id="author-1"><persName><forename type="first">Andreas</forename><surname>Defant</surname></persName><affiliation>Institut of Mathematics, Carl von Ossietzky Universität, 26111, Oldenburg, Germany</affiliation></author><author xml:id="author-2"><persName><forename type="first">Leonhard</forename><surname>Frerick</surname></persName><affiliation>Fachbereich IV - Mathematik, Universität Trier, 54294, Trier, Germany</affiliation></author></analytic><monogr><title level="j">Journal für die reine und angewandte Mathematik (Crelles Journal)</title><title level="j" type="abbrev">Journal für die reine und angewandte Mathematik (Crelles Journal)</title><idno type="pISSN">0075-4102</idno><idno type="eISSN">1435-5345</idno><imprint><publisher>Walter de Gruyter GmbH & Co. KG</publisher><date type="published" when="2011-11"></date><biblScope unit="volume">2011</biblScope><biblScope unit="issue">660</biblScope><biblScope unit="page" from="131">131</biblScope><biblScope unit="page" to="147">147</biblScope></imprint></monogr><idno type="istex">3A193EF5E25BA4E6AF3BCC89E9F55F0A6984C7C9</idno><idno type="DOI">10.1515/crelle.2011.080</idno><idno type="ArticleID">crll.2011.660.131</idno><idno type="pdf">crelle.2011.080.pdf</idno></biblStruct></sourceDesc></fileDesc><profileDesc><creation><date>2011-06-28</date></creation><langUsage><language ident="en">en</language></langUsage><abstract xml:lang="en"><p>By a classical result due to Aizenberg, Boas and Khavinson the Bohr radius of the unit ball in the Minkowski space , 1 ≦ p ≦ ∞, is up to an absolute constant ≦ (log n/n)1–1/min(p, 2). Our main result shows that this estimate is optimal. For p = ∞, this was recently proved in [Defant, Frerick, Ortega-Cerdà, Ounaies and Seip, Ann. Math. 174: 1–13, 2011] as a consequence of the hypercontractivity of the Bohnenblust–Hille inequality for polynomials. Using substantially different methods from local Banach space theory, we give a proof which covers the full scale 1 ≦ p ≦ ∞.</p></abstract></profileDesc><revisionDesc><change when="2011-06-28">Created</change><change when="2011-11">Published</change><change xml:id="refBibs-istex" who="#ISTEX-API" when="2017-01-17">References added</change></revisionDesc></teiHeader></istex:fulltextTEI><json:item><extension>txt</extension><original>false</original><mimetype>text/plain</mimetype><uri>https://api.istex.fr/document/3A193EF5E25BA4E6AF3BCC89E9F55F0A6984C7C9/fulltext/txt</uri></json:item></fulltext><metadata><istex:metadataXml wicri:clean="corpus degruyter-journals" wicri:toSee="no header"><istex:xmlDeclaration>version="1.0" encoding="UTF-8"</istex:xmlDeclaration><istex:docType PUBLIC="-//Atypon//DTD Atypon Systems Archival NLM DTD Suite v2.2.0 20090301//EN" URI="nlm-dtd/archivearticle.dtd" name="istex:docType"></istex:docType><istex:document><article article-type="research-article" xml:lang="en"><front><journal-meta><journal-id journal-id-type="publisher-id">crll</journal-id><abbrev-journal-title abbrev-type="full">Journal für die reine und angewandte Mathematik (Crelles Journal)</abbrev-journal-title><issn pub-type="ppub">0075-4102</issn><issn pub-type="epub">1435-5345</issn><publisher><publisher-name>Walter de Gruyter GmbH & Co. KG</publisher-name></publisher></journal-meta><article-meta><article-id pub-id-type="publisher-id">crll.2011.660.131</article-id><article-id pub-id-type="doi">10.1515/crelle.2011.080</article-id><title-group><article-title>The Bohr radius of the unit ball of <inline-graphic xlink:href="crelle.2011.080_eq1.gif"></inline-graphic></article-title></title-group><contrib-group><contrib contrib-type="author"><name name-style="western"><given-names>Andreas</given-names><x> </x><surname>Defant</surname></name><email>defant@mathematik.uni-oldenburg.de</email><xref ref-type="aff" rid="aff1"><sup>1</sup></xref><x>, </x></contrib><contrib contrib-type="author"><name name-style="western"><given-names>Leonhard</given-names><x> </x><surname>Frerick</surname></name><email>frerick@uni-trier.de</email><xref ref-type="aff" rid="aff2"><sup>2</sup></xref></contrib><aff id="aff1"><sup>1</sup>Institut of Mathematics, Carl von Ossietzky Universität, 26111, Oldenburg, Germany</aff><aff id="aff2"><sup>2</sup>Fachbereich IV - Mathematik, Universität Trier, 54294, Trier, Germany</aff></contrib-group><pub-date pub-type="ppub"><month>November</month><year>2011</year></pub-date><pub-date pub-type="epub"><day>28</day><month>06</month><year>2011</year></pub-date><volume>2011</volume><issue>660</issue><fpage>131</fpage><lpage>147</lpage><history><date date-type="received"><day>12</day><month>02</month><year>2010</year><string-date>Eingegangen 12. Februar 2010.</string-date></date><date date-type="rev-recd"><day>11</day><month>08</month><year>2010</year><string-date>in revidierter Fassung 11. August 2010.</string-date></date></history><copyright-statement>© Walter de Gruyter Berlin · New York 2011</copyright-statement><copyright-year>2011</copyright-year><related-article related-article-type="pdf" xlink:href="crelle.2011.080.pdf"></related-article><abstract><title>Abstract</title><p>By a classical result due to Aizenberg, Boas and Khavinson the Bohr radius <inline-graphic xlink:href="crelle.2011.080_eq2.gif"></inline-graphic> of the unit ball in the Minkowski space <inline-graphic xlink:href="crelle.2011.080_eq3.gif"></inline-graphic>, 1 ≦ <italic>p</italic> ≦ ∞, is up to an absolute constant ≦ (log <italic>n</italic>/<italic>n</italic>)<sup>1–1/min(<italic>p</italic>, 2)</sup>. Our main result shows that this estimate is optimal. For <italic>p</italic> = ∞, this was recently proved in [Defant, Frerick, Ortega-Cerdà, Ounaies and Seip, Ann. Math. 174: 1–13, 2011] as a consequence of the hypercontractivity of the Bohnenblust–Hille inequality for polynomials. Using substantially different methods from local Banach space theory, we give a proof which covers the full scale 1 ≦ <italic>p</italic> ≦ ∞.</p></abstract></article-meta></front></article></istex:document></istex:metadataXml><mods version="3.6"><titleInfo lang="en"><title>The Bohr radius of the unit ball of</title></titleInfo><titleInfo type="alternative" lang="en" contentType="CDATA"><title>The Bohr radius of the unit ball of</title></titleInfo><name type="personal"><namePart type="given">Andreas</namePart><namePart type="family">Defant</namePart><affiliation>Institut of Mathematics, Carl von Ossietzky Universität, 26111, Oldenburg, Germany</affiliation><role><roleTerm type="text">author</roleTerm></role></name><name type="personal"><namePart type="given">Leonhard</namePart><namePart type="family">Frerick</namePart><affiliation>Fachbereich IV - Mathematik, Universität Trier, 54294, Trier, Germany</affiliation><role><roleTerm type="text">author</roleTerm></role></name><typeOfResource>text</typeOfResource><genre type="research-article" displayLabel="research-article"></genre><originInfo><publisher>Walter de Gruyter GmbH & Co. KG</publisher><dateIssued encoding="w3cdtf">2011-11</dateIssued><dateCreated encoding="w3cdtf">2011-06-28</dateCreated><copyrightDate encoding="w3cdtf">2011</copyrightDate></originInfo><language><languageTerm type="code" authority="iso639-2b">eng</languageTerm><languageTerm type="code" authority="rfc3066">en</languageTerm></language><physicalDescription><internetMediaType>text/html</internetMediaType></physicalDescription><abstract lang="en">By a classical result due to Aizenberg, Boas and Khavinson the Bohr radius of the unit ball in the Minkowski space , 1 ≦ p ≦ ∞, is up to an absolute constant ≦ (log n/n)1–1/min(p, 2). Our main result shows that this estimate is optimal. For p = ∞, this was recently proved in [Defant, Frerick, Ortega-Cerdà, Ounaies and Seip, Ann. Math. 174: 1–13, 2011] as a consequence of the hypercontractivity of the Bohnenblust–Hille inequality for polynomials. Using substantially different methods from local Banach space theory, we give a proof which covers the full scale 1 ≦ p ≦ ∞.</abstract><relatedItem type="host"><titleInfo><title>Journal für die reine und angewandte Mathematik (Crelles Journal)</title></titleInfo><titleInfo type="abbreviated"><title>Journal für die reine und angewandte Mathematik (Crelles Journal)</title></titleInfo><genre type="journal">journal</genre><identifier type="ISSN">0075-4102</identifier><identifier type="eISSN">1435-5345</identifier><identifier type="PublisherID">crll</identifier><part><date>2011</date><detail type="volume"><caption>vol.</caption><number>2011</number></detail><detail type="issue"><caption>no.</caption><number>660</number></detail><extent unit="pages"><start>131</start><end>147</end></extent></part></relatedItem><identifier type="istex">3A193EF5E25BA4E6AF3BCC89E9F55F0A6984C7C9</identifier><identifier type="DOI">10.1515/crelle.2011.080</identifier><identifier type="ArticleID">crll.2011.660.131</identifier><identifier type="pdf">crelle.2011.080.pdf</identifier><accessCondition type="use and reproduction" contentType="copyright">© Walter de Gruyter Berlin · New York 2011, 2011</accessCondition><recordInfo><recordContentSource>De Gruyter</recordContentSource></recordInfo></mods></metadata><annexes><json:item><extension>gif</extension><original>true</original><mimetype>image/gif</mimetype><uri>https://api.istex.fr/document/3A193EF5E25BA4E6AF3BCC89E9F55F0A6984C7C9/annexes/gif</uri></json:item></annexes><serie></serie></istex></record>Pour manipuler ce document sous Unix (Dilib)
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