<?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>0034-7426</journal-id>
<journal-title><![CDATA[Revista Colombiana de Matemáticas]]></journal-title>
<abbrev-journal-title><![CDATA[Rev.colomb.mat.]]></abbrev-journal-title>
<issn>0034-7426</issn>
<publisher>
<publisher-name><![CDATA[Universidad Nacional de Colombia y Sociedad Colombiana de Matemáticas]]></publisher-name>
</publisher>
</journal-meta>
<article-meta>
<article-id>S0034-74262021000100021</article-id>
<article-id pub-id-type="doi">10.15446/recolma.v55n1.99097</article-id>
<title-group>
<article-title xml:lang="en"><![CDATA[Boundedness of the Maximal Function of the Ornstein-Uhlenbeck semigroup on variable Lebesgue spaces with respect to the Gaussian measure and consequences]]></article-title>
<article-title xml:lang="es"><![CDATA[Acotación de la Función Maximal del Semigrupo de Ornstein-Uhlenbeck en Espacios de Lebesgue Variables y sus consecuencias]]></article-title>
</title-group>
<contrib-group>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Moreno]]></surname>
<given-names><![CDATA[Jorge]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Pineda]]></surname>
<given-names><![CDATA[Ebner]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Urbina]]></surname>
<given-names><![CDATA[Wilfredo]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
</contrib-group>
<aff id="Af1">
<institution><![CDATA[,Universidad Centro Occidental Lisandro Alvarado  ]]></institution>
<addr-line><![CDATA[Barquisimeto ]]></addr-line>
<country>Venezuela</country>
</aff>
<aff id="Af2">
<institution><![CDATA[,Escuela Superior Politécnica del Litoral  ]]></institution>
<addr-line><![CDATA[Guayaquil ]]></addr-line>
<country>Ecuador</country>
</aff>
<aff id="Af3">
<institution><![CDATA[,Roosevelt University  ]]></institution>
<addr-line><![CDATA[Chicago ]]></addr-line>
<country>USA</country>
</aff>
<pub-date pub-type="pub">
<day>00</day>
<month>06</month>
<year>2021</year>
</pub-date>
<pub-date pub-type="epub">
<day>00</day>
<month>06</month>
<year>2021</year>
</pub-date>
<volume>55</volume>
<numero>1</numero>
<fpage>21</fpage>
<lpage>41</lpage>
<copyright-statement/>
<copyright-year/>
<self-uri xlink:href="http://www.scielo.org.co/scielo.php?script=sci_arttext&amp;pid=S0034-74262021000100021&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.org.co/scielo.php?script=sci_abstract&amp;pid=S0034-74262021000100021&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.org.co/scielo.php?script=sci_pdf&amp;pid=S0034-74262021000100021&amp;lng=en&amp;nrm=iso"></self-uri><abstract abstract-type="short" xml:lang="en"><p><![CDATA[Abstract The main result of this paper is the proof of the boundedness of the Maximal Function T* of the Ornstein-Uhlenbeck semigroup {T  t } t&#8805;0 in &#8477; d , on Gaussian variable Lebesgue spaces L  p(ˇ) (&#947; d ), under a condition of regularity on p(ˇ) following [5] and [8]. As an immediate consequence of that result, the Lp(ˇ)(&#947; d )-boundedness of the Ornstein-Uhlenbeck semigroup {T  t } t&#8805;0 in &#8477; d is obtained. Another consequence of that result is the Lp(ˇ)(&#947; d )-boundedness of the Poisson-Hermite semigroup and the Lp(ˇ)(&#947; d )-boundedness of the Gaussian Bessel potentials of order &#946; &gt; 0.]]></p></abstract>
<abstract abstract-type="short" xml:lang="es"><p><![CDATA[Resumen El principal resultado de este artículo es la prueba de la acotación de la Función Maximal T* del semigrupo de Ornstein-Uhlenbeck {T  t } t&#8805;0 en &#8477; d sobre espacios de Lebesgue variables respecto de la medida Gaussiana L  p(ˇ) (&#947; d ), asumiendo una condición de regularidad en p(ˇ) siguiendo [5] y [8]. Como consecuencia inmediata de éste resultado se obtiene la acotación- L  p(ˇ) (&#947; d ) del semigrupo de Ornstein-Uhlenbeck {T  t } t&#8805;0 en &#8477; d . Otras consecuencias del resultado es la acotación L  p(ˇ) (&#947; d ) del semigrupo Poisson-Hermite y la acotación L  p(ˇ) (&#947; d ) de los potenciales de Bessel Gaussianos de orden &#946; &gt; 0.]]></p></abstract>
<kwd-group>
<kwd lng="en"><![CDATA[Gaussian harmonic analysis]]></kwd>
<kwd lng="en"><![CDATA[variable Lebesgue spaces]]></kwd>
<kwd lng="en"><![CDATA[Ornstein-Uhlenbeck semigroup]]></kwd>
<kwd lng="es"><![CDATA[Análisis Armónico Gaussiano]]></kwd>
<kwd lng="es"><![CDATA[espacios de Lebesgue Gaussianos]]></kwd>
<kwd lng="es"><![CDATA[semigrupo de Ornstein-Uhlenbeck]]></kwd>
</kwd-group>
</article-meta>
</front><back>
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