<?xml version="1.0" encoding="utf-8"?>
<TEI xmlns="http://www.tei-c.org/ns/1.0" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xmlns:hal="http://hal.archives-ouvertes.fr/" xmlns:gml="http://www.opengis.net/gml/3.3/" xmlns:gmlce="http://www.opengis.net/gml/3.3/ce" version="1.1" xsi:schemaLocation="http://www.tei-c.org/ns/1.0 http://api.archives-ouvertes.fr/documents/aofr-sword.xsd">
  <teiHeader>
    <fileDesc>
      <titleStmt>
        <title>HAL TEI export of hal-00243816</title>
      </titleStmt>
      <publicationStmt>
        <distributor>CCSD</distributor>
        <availability status="restricted">
          <licence target="https://creativecommons.org/publicdomain/zero/1.0/">CC0 1.0 - Universal</licence>
        </availability>
        <date when="2026-05-18T16:23:59+02:00"/>
      </publicationStmt>
      <sourceDesc>
        <p part="N">HAL API Platform</p>
      </sourceDesc>
    </fileDesc>
  </teiHeader>
  <text>
    <body>
      <listBibl>
        <biblFull>
          <titleStmt>
            <title xml:lang="en">Interpolation of Sobolev spaces, Littlewood-Paley inequalities and Riesz transforms on graphs</title>
            <author role="aut">
              <persName>
                <forename type="first">Nadine</forename>
                <surname>Badr</surname>
              </persName>
              <email type="md5">b49ffde03a7cb5220b7eb2f15c6f3f88</email>
              <email type="domain">math.u-psud.fr</email>
              <idno type="idhal" notation="numeric">856374</idno>
              <idno type="halauthorid" notation="string">287332-856374</idno>
              <affiliation ref="#struct-40"/>
            </author>
            <author role="crp">
              <persName>
                <forename type="first">Emmanuel</forename>
                <surname>Russ</surname>
              </persName>
              <email type="md5">f411ad53289a6a35f09f1550488d150e</email>
              <email type="domain">univ-grenoble-alpes.fr</email>
              <idno type="idhal" notation="string">emmanuel-russ</idno>
              <idno type="idhal" notation="numeric">15582</idno>
              <idno type="halauthorid" notation="string">27259-15582</idno>
              <idno type="IDREF">https://www.idref.fr/152683615</idno>
              <idno type="ORCID">https://orcid.org/0000-0002-6147-7078</idno>
              <affiliation ref="#struct-84"/>
            </author>
            <editor role="depositor">
              <persName>
                <forename>Emmanuel</forename>
                <surname>Russ</surname>
              </persName>
              <email type="md5">14f7d2047a7f7c2f62966e14a07f22a3</email>
              <email type="domain">univ-amu.fr</email>
            </editor>
          </titleStmt>
          <editionStmt>
            <edition n="v1" type="current">
              <date type="whenSubmitted">2008-02-07 08:55:21</date>
              <date type="whenWritten">2008-02-07</date>
              <date type="whenModified">2025-12-22 10:14:11</date>
              <date type="whenReleased">2008-02-07 09:25:07</date>
              <date type="whenProduced">2009</date>
              <date type="whenEndEmbargoed">2008-02-07</date>
              <ref type="file" target="https://hal.science/hal-00243816v1/document">
                <date notBefore="2008-02-07"/>
              </ref>
              <ref type="file" subtype="author" n="1" target="https://hal.science/hal-00243816v1/file/Rieszgraph.pdf" id="file-243816-184193">
                <date notBefore="2008-02-07"/>
              </ref>
              <ref type="externalLink" target="http://arxiv.org/pdf/0802.0922"/>
            </edition>
            <respStmt>
              <resp>contributor</resp>
              <name key="383405">
                <persName>
                  <forename>Emmanuel</forename>
                  <surname>Russ</surname>
                </persName>
                <email type="md5">14f7d2047a7f7c2f62966e14a07f22a3</email>
                <email type="domain">univ-amu.fr</email>
              </name>
            </respStmt>
          </editionStmt>
          <publicationStmt>
            <distributor>CCSD</distributor>
            <idno type="halId">hal-00243816</idno>
            <idno type="halUri">https://hal.science/hal-00243816</idno>
            <idno type="halBibtex">badr:hal-00243816</idno>
            <idno type="halRefHtml">&lt;i&gt;Publicacions Matemàtiques&lt;/i&gt;, 2009, 53 (2), pp.273-328</idno>
            <idno type="halRef">Publicacions Matemàtiques, 2009, 53 (2), pp.273-328</idno>
            <availability status="restricted">
              <licence target="https://about.hal.science/hal-authorisation-v1/">HAL Authorization<ref corresp="#file-243816-184193"/></licence>
            </availability>
          </publicationStmt>
          <seriesStmt>
            <idno type="stamp" n="LATP" corresp="I2M">Laboratoire d'Analyse, Topologie, Probabilités</idno>
            <idno type="stamp" n="CNRS">CNRS - Centre national de la recherche scientifique</idno>
            <idno type="stamp" n="UNIV-AMU">Aix Marseille Université</idno>
            <idno type="stamp" n="UNIV-PSUD">Université Paris Sud - Paris XI</idno>
            <idno type="stamp" n="LM-ORSAY">Laboratoire de Mathématiques d'Orsay</idno>
            <idno type="stamp" n="I2M">Institut de Mathématiques de Marseille</idno>
            <idno type="stamp" n="TDS-MACS">Réseau de recherche en Théorie des Systèmes Distribués, Modélisation, Analyse et Contrôle des Systèmes</idno>
            <idno type="stamp" n="UNIV-PARIS-SACLAY">Université Paris-Saclay</idno>
            <idno type="stamp" n="UNIV-PSUD-SACLAY" corresp="UNIV-PARIS-SACLAY">Université Paris Sud pour Paris Saclay</idno>
            <idno type="stamp" n="GS-MATHEMATIQUES">Graduate School Mathématiques</idno>
          </seriesStmt>
          <notesStmt>
            <note type="audience" n="2">International</note>
            <note type="popular" n="0">No</note>
            <note type="peer" n="1">Yes</note>
          </notesStmt>
          <sourceDesc>
            <biblStruct>
              <analytic>
                <title xml:lang="en">Interpolation of Sobolev spaces, Littlewood-Paley inequalities and Riesz transforms on graphs</title>
                <author role="aut">
                  <persName>
                    <forename type="first">Nadine</forename>
                    <surname>Badr</surname>
                  </persName>
                  <email type="md5">b49ffde03a7cb5220b7eb2f15c6f3f88</email>
                  <email type="domain">math.u-psud.fr</email>
                  <idno type="idhal" notation="numeric">856374</idno>
                  <idno type="halauthorid" notation="string">287332-856374</idno>
                  <affiliation ref="#struct-40"/>
                </author>
                <author role="crp">
                  <persName>
                    <forename type="first">Emmanuel</forename>
                    <surname>Russ</surname>
                  </persName>
                  <email type="md5">f411ad53289a6a35f09f1550488d150e</email>
                  <email type="domain">univ-grenoble-alpes.fr</email>
                  <idno type="idhal" notation="string">emmanuel-russ</idno>
                  <idno type="idhal" notation="numeric">15582</idno>
                  <idno type="halauthorid" notation="string">27259-15582</idno>
                  <idno type="IDREF">https://www.idref.fr/152683615</idno>
                  <idno type="ORCID">https://orcid.org/0000-0002-6147-7078</idno>
                  <affiliation ref="#struct-84"/>
                </author>
              </analytic>
              <monogr>
                <idno type="halJournalId" status="VALID">24040</idno>
                <idno type="issn">0210-2978</idno>
                <idno type="eissn">2014-4369</idno>
                <title level="j">Publicacions Matemàtiques</title>
                <imprint>
                  <publisher>Universitat Autònoma de Barcelona</publisher>
                  <biblScope unit="volume">53</biblScope>
                  <biblScope unit="issue">2</biblScope>
                  <biblScope unit="pp">273-328</biblScope>
                  <date type="datePub">2009</date>
                </imprint>
              </monogr>
              <idno type="arxiv">0802.0922</idno>
            </biblStruct>
          </sourceDesc>
          <profileDesc>
            <langUsage>
              <language ident="en">English</language>
            </langUsage>
            <textClass>
              <keywords scheme="author">
                <term xml:lang="en">interpolation</term>
                <term xml:lang="en">Graphs</term>
                <term xml:lang="en">discrete Laplacian</term>
                <term xml:lang="en">Riesz transforms</term>
                <term xml:lang="en">Littlewood-Paley inequalities</term>
                <term xml:lang="en">Sobolev spaces</term>
                <term xml:lang="en">interpolation.</term>
              </keywords>
              <classCode scheme="classification">AMS: Primary: 60J10. Secondary: 42B20, 42B25.</classCode>
              <classCode scheme="halDomain" n="math.math-ap">Mathematics [math]/Analysis of PDEs [math.AP]</classCode>
              <classCode scheme="halTypology" n="ART">Journal articles</classCode>
              <classCode scheme="halOldTypology" n="ART">Journal articles</classCode>
              <classCode scheme="halTreeTypology" n="ART">Journal articles</classCode>
            </textClass>
            <abstract xml:lang="en">
              <p>Let $\Gamma$ be a graph endowed with a reversible Markov kernel $p$, and $P$ the associated operator, defined by $Pf(x)=\sum_y p(x,y)f(y)$. Denote by $\nabla$ the discrete gradient. We give necessary and/or sufficient conditions on $\Gamma$ in order to compare $\left\Vert \nabla f\right\Vert_{p}$ and $\left\Vert (I-P)^{1/2}f\right\Vert_{p}$ uniformly in $f$ for $12$. The proofs rely on recent techniques developed to handle operators beyond the class of Calderón-Zygmund operators. For our purpose, we also prove Littlewood-Paley inequalities and interpolation results for Sobolev spaces in this context, which are of independent interest.</p>
            </abstract>
          </profileDesc>
        </biblFull>
      </listBibl>
    </body>
    <back>
      <listOrg type="structures">
        <org type="laboratory" xml:id="struct-40" status="OLD">
          <orgName>Laboratoire de Mathématiques d'Orsay</orgName>
          <orgName type="acronym">LMO</orgName>
          <date type="end">2019-12-31</date>
          <desc>
            <address>
              <addrLine>Bâtiment 307, rue Michel Magat, Faculté des sciences, Université Paris-Saclay, 91405 Orsay Cédex</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">http://www.math.u-psud.fr</ref>
          </desc>
          <listRelation>
            <relation active="#struct-92966" type="direct"/>
            <relation name="UMR8628" active="#struct-441569" type="direct"/>
          </listRelation>
        </org>
        <org type="laboratory" xml:id="struct-84" status="OLD">
          <idno type="RNSR">199612403D</idno>
          <orgName>Laboratoire d'Analyse, Topologie, Probabilités</orgName>
          <orgName type="acronym">LATP</orgName>
          <date type="start">2008-01-01</date>
          <date type="end">2011-12-31</date>
          <desc>
            <address>
              <addrLine>39 rue Joliot-Curie 13453 Marseille Cedex 13</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">http://www.latp.univ-mrs.fr</ref>
          </desc>
          <listRelation>
            <relation active="#struct-27501" type="direct"/>
            <relation active="#struct-92823" type="direct"/>
            <relation name="UMR6632" active="#struct-441569" type="direct"/>
          </listRelation>
        </org>
        <org type="institution" xml:id="struct-92966" status="OLD">
          <idno type="ROR">https://ror.org/028rypz17</idno>
          <orgName>Université Paris-Sud - Paris 11</orgName>
          <orgName type="acronym">UP11</orgName>
          <date type="end">2019-12-31</date>
          <desc>
            <address>
              <addrLine>Bâtiment 300 - 91405 Orsay cedex</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">http://www.u-psud.fr/</ref>
          </desc>
        </org>
        <org type="regroupinstitution" xml:id="struct-441569" status="VALID">
          <idno type="IdRef">02636817X</idno>
          <idno type="ISNI">0000000122597504</idno>
          <idno type="ROR">https://ror.org/02feahw73</idno>
          <orgName>Centre National de la Recherche Scientifique</orgName>
          <orgName type="acronym">CNRS</orgName>
          <date type="start">1939-10-19</date>
          <desc>
            <address>
              <country key="FR"/>
            </address>
            <ref type="url">https://www.cnrs.fr/</ref>
          </desc>
        </org>
        <org type="institution" xml:id="struct-27501" status="OLD">
          <idno type="IdRef">026403153</idno>
          <orgName>Université Paul Cézanne - Aix-Marseille 3</orgName>
          <date type="end">2011</date>
          <desc>
            <address>
              <addrLine>3, avenue Robert Schumann - 13628 Aix-en-Provence cedex 1</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">http://www.univ-cezanne.fr/</ref>
          </desc>
        </org>
        <org type="institution" xml:id="struct-92823" status="OLD">
          <idno type="IdRef">026403781</idno>
          <orgName>Université de Provence - Aix-Marseille 1</orgName>
          <date type="end">2011-12-31</date>
          <desc>
            <address>
              <addrLine>3, place Victor Hugo - 13331 Marseille Cedex 03</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">http://www.univ-provence.fr/</ref>
          </desc>
        </org>
      </listOrg>
    </back>
  </text>
</TEI>