<?xml version="1.0" encoding="ISO-8859-1"?><article xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance">
<front>
<journal-meta>
<journal-id>0120-419X</journal-id>
<journal-title><![CDATA[Revista Integración]]></journal-title>
<abbrev-journal-title><![CDATA[Integración - UIS]]></abbrev-journal-title>
<issn>0120-419X</issn>
<publisher>
<publisher-name><![CDATA[Universidad Industrial de Santander]]></publisher-name>
</publisher>
</journal-meta>
<article-meta>
<article-id>S0120-419X2024000100001</article-id>
<article-id pub-id-type="doi">10.18273/revint.v42n1-2024001</article-id>
<title-group>
<article-title xml:lang="en"><![CDATA[Boundedness of the Hilbert Transform on Rearrangement Invariant Spaces]]></article-title>
<article-title xml:lang="es"><![CDATA[Acotación de la transformada de Hilbert en espacios invariantes por reordenamiento]]></article-title>
</title-group>
<contrib-group>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Castillo]]></surname>
<given-names><![CDATA[René Erlin]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Chaparro]]></surname>
<given-names><![CDATA[Héctor Camilo]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
</contrib-group>
<aff id="Af1">
<institution><![CDATA[,Universidad Nacional de Colombia Departamento de Matemáticas ]]></institution>
<addr-line><![CDATA[Bogotá ]]></addr-line>
<country>Colombia</country>
</aff>
<aff id="Af2">
<institution><![CDATA[,Universidad de Cartagena  ]]></institution>
<addr-line><![CDATA[Cartagena de Indias ]]></addr-line>
<country>Colombia</country>
</aff>
<pub-date pub-type="pub">
<day>00</day>
<month>06</month>
<year>2024</year>
</pub-date>
<pub-date pub-type="epub">
<day>00</day>
<month>06</month>
<year>2024</year>
</pub-date>
<volume>42</volume>
<numero>1</numero>
<fpage>1</fpage>
<lpage>21</lpage>
<copyright-statement/>
<copyright-year/>
<self-uri xlink:href="http://www.scielo.org.co/scielo.php?script=sci_arttext&amp;pid=S0120-419X2024000100001&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.org.co/scielo.php?script=sci_abstract&amp;pid=S0120-419X2024000100001&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.org.co/scielo.php?script=sci_pdf&amp;pid=S0120-419X2024000100001&amp;lng=en&amp;nrm=iso"></self-uri><abstract abstract-type="short" xml:lang="en"><p><![CDATA[Abstract. In this self-contained review, the aspects about the applications of decreasing rearrangement techniques to the analysis of pointwise estimates for the Hilbert transform are analyzed. We make a consistent revision of these techniques in the proof of the Lp-boundedness of the Hilbert transform. This is a celebrated theorem due to M. Riesz.  MSC2020:  44A15, 47B38, 28-02.]]></p></abstract>
<abstract abstract-type="short" xml:lang="es"><p><![CDATA[Resumen. En esta revisión autocontenida, se analizan los aspectos sobre las aplicaciones de técnicas de reordenamiento decreciente para el análisis de estimaciones punto a punto para la transformada de Hilbert. Realizamos una revisión consistente de estas técnicas en la demostración de la acotación en Lp de la transformada de Hilbert. Este es un teorema célebre debido a M. Riesz.]]></p></abstract>
<kwd-group>
<kwd lng="en"><![CDATA[Hilbert transform]]></kwd>
<kwd lng="en"><![CDATA[distribution function]]></kwd>
<kwd lng="en"><![CDATA[decreasing rearregement]]></kwd>
<kwd lng="en"><![CDATA[Hardy&#8217;s inequality]]></kwd>
<kwd lng="es"><![CDATA[Transformada de Hilbert]]></kwd>
<kwd lng="es"><![CDATA[función distribución]]></kwd>
<kwd lng="es"><![CDATA[reordenamien-to decreciente]]></kwd>
<kwd lng="es"><![CDATA[desigualdad de Hardy]]></kwd>
</kwd-group>
</article-meta>
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