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  <doc>
    <id>1628</id>
    <completedYear>2023</completedYear>
    <publishedYear>2023</publishedYear>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst>5493</pageFirst>
    <pageLast>5512</pageLast>
    <pageNumber>20 Seiten</pageNumber>
    <edition/>
    <issue>12</issue>
    <volume>296</volume>
    <type>article</type>
    <publisherName>Wiley</publisherName>
    <publisherPlace>Hoboken</publisherPlace>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>2023-03-29</completedDate>
    <publishedDate>2023-03-29</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Hölder’s inequality and its reverse — a probabilistic point of view</title>
    <abstract language="eng">In this article, we take a probabilistic look at Hölder's inequality, considering the ratio of terms in the classical Hölder inequality for random vectors in ℝ𝑛. We prove a central limit theorem for this ratio, which then allows us to reverse the inequality up to a multiplicative constant with high probability. The models of randomness include the uniform distribution on 𝓁𝑛𝑝 balls and spheres. We also provide a Berry–Esseen–type result and prove a large and a moderate deviation principle for the suitably normalized Hölder ratio.</abstract>
    <parentTitle language="deu">Mathematische Nachrichten</parentTitle>
    <identifier type="doi">10.1002/mana.202200411</identifier>
    <identifier type="urn">urn:nbn:de:101:1-2023062315175042989607</identifier>
    <enrichment key="opus.doi.autoCreate">false</enrichment>
    <enrichment key="opus.urn.autoCreate">false</enrichment>
    <enrichment key="review.accepted_by">2</enrichment>
    <licence>Creative Commons - CC BY - Namensnennung 4.0 International</licence>
    <author>Lorenz Frühwirth</author>
    <author>Joscha Prochno</author>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Berry–Esseen bound</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>central limit theorem</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Hölder’s inequality</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>𝓁 𝑛 𝑝 ball</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>large deviation principle</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>moderate deviation principle</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>reverse inequality</value>
    </subject>
    <collection role="ddc" number="510">Mathematik</collection>
    <collection role="open_access" number="">open_access</collection>
    <collection role="institutes" number="">Fakultät für Informatik und Mathematik</collection>
    <collection role="Transformationsvertrag" number="">DEAL Wiley</collection>
    <file>https://opus4.kobv.de/opus4-uni-passau/files/1628/Fruehwirth_Hoelders-inequality.pdf</file>
  </doc>
</export-example>
