<?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>S0120-419X2018000200151</article-id>
<article-id pub-id-type="doi">10.18273/revint.v36n2-2018006</article-id>
<title-group>
<article-title xml:lang="en"><![CDATA[Multilinear analysis for discrete and periodic pseudo-differential operators in Lp-spaces]]></article-title>
<article-title xml:lang="es"><![CDATA[Análisis multilineal para operadores pseudodiferenciales periódicos y discretos en espacios Lp]]></article-title>
</title-group>
<contrib-group>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Cardona]]></surname>
<given-names><![CDATA[Duván]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Kumar]]></surname>
<given-names><![CDATA[Vishvesh]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
</contrib-group>
<aff id="Af1">
<institution><![CDATA[,Pontificia Universidad Javeriana Department of Mathematics ]]></institution>
<addr-line><![CDATA[Bogotá ]]></addr-line>
<country>Colombia</country>
</aff>
<aff id="Af2">
<institution><![CDATA[,Indian Institute of Technology Delhi Department of Mathematics ]]></institution>
<addr-line><![CDATA[ ]]></addr-line>
<country>India</country>
</aff>
<pub-date pub-type="pub">
<day>00</day>
<month>12</month>
<year>2018</year>
</pub-date>
<pub-date pub-type="epub">
<day>00</day>
<month>12</month>
<year>2018</year>
</pub-date>
<volume>36</volume>
<numero>2</numero>
<fpage>151</fpage>
<lpage>164</lpage>
<copyright-statement/>
<copyright-year/>
<self-uri xlink:href="http://www.scielo.org.co/scielo.php?script=sci_arttext&amp;pid=S0120-419X2018000200151&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.org.co/scielo.php?script=sci_abstract&amp;pid=S0120-419X2018000200151&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.org.co/scielo.php?script=sci_pdf&amp;pid=S0120-419X2018000200151&amp;lng=en&amp;nrm=iso"></self-uri><abstract abstract-type="short" xml:lang="en"><p><![CDATA[Abstract In this note we announce our investigation on the  L  p properties for periodic and discrete multilinear pseudo-differential operators. First, we review the periodic analysis of multilinear pseudo-differential operators by showing classical multilinear Fourier multipliers theorems (proved by Coifman and Meyer, Tomita, Miyachi, Fujita, Grafakos, Tao, etc.) in the context of periodic and discrete multilinear pseudo-differential operators. For this, we use the periodic analysis of pseudo-differential operators developed by Ruzhansky and Turunen. The s-nuclearity, 0 &lt; s &#8804; 1, for the discrete and periodic multilinear pseudo-differential operators will be investigated. To do so, we classify those s-nuclear, 0 &lt; s &#8804; 1, multilinear integral operators on arbitrary Lebesgue spaces defined on &#963;-finite measures spaces. Finally, we present some applications of our analysis to deduce the periodic Kato-Ponce inequality and to examine the s-nuclearity of multilinear Bessel potentials as well as the s-nuclearity of periodic Fourier integral operators admitting suitable types of singularities.  MSC2010: 58J40, 47B10, 47G30, 35S30.]]></p></abstract>
<abstract abstract-type="short" xml:lang="es"><p><![CDATA[Resumen En esta nota anunciamos los resultados de nuestra investigación sobre las propiedades  L  p de operadores pseudodiferenciales multilineales periódicos y/o discretos. Primero, revisaremos el análisis multilineal de tales operadores mostrando versiones análogas de los teoremas clásicos disponibles en el análisis multilineal euclidiano (debidos a Coifman y Meyer, Tomita, Miyachi, Fujita, Grafakos, Tao, etc.), pero, en el contexto de operadores periódicos y/o discretos. Se caracterizará la s-nuclearidad, 0 &lt; s &#8804; 1, para operadores multilineales pseudodiferenciales periódicos y/o discretos. Para cumplir este objetivo se clasificarán aquellos operadores lineales s-nucleares, 0 &lt; s &#8804; 1, multilineales con núcleo, sobre espacios de Lebesgue arbitrarios definidos en espacios de medida &#963;-finitos. Finalmente, como aplicación de los resultados presentados se obtiene la versión periódica de la desigualdad de Kato-Ponce, y se examina la s-nuclearidad de potenciales de Bessel lineales y multilineales, como también la s-nuclearidad de operadores integrales de Fourier periódicos admitiendo símbolos con tipos adecuados de singularidad.]]></p></abstract>
<kwd-group>
<kwd lng="en"><![CDATA[Pseudo-differential operator]]></kwd>
<kwd lng="en"><![CDATA[discrete operator]]></kwd>
<kwd lng="en"><![CDATA[periodic operator]]></kwd>
<kwd lng="en"><![CDATA[nuclearity]]></kwd>
<kwd lng="en"><![CDATA[boundedness]]></kwd>
<kwd lng="en"><![CDATA[Fourier integral operator]]></kwd>
<kwd lng="en"><![CDATA[multilinear analysis]]></kwd>
<kwd lng="es"><![CDATA[Operador pseudo-diferencial]]></kwd>
<kwd lng="es"><![CDATA[operador discreto]]></kwd>
<kwd lng="es"><![CDATA[operador periódico]]></kwd>
<kwd lng="es"><![CDATA[nuclearidad]]></kwd>
<kwd lng="es"><![CDATA[continuidad]]></kwd>
<kwd lng="es"><![CDATA[operador integral de Fourier]]></kwd>
<kwd lng="es"><![CDATA[Análisis multilineal]]></kwd>
</kwd-group>
</article-meta>
</front><back>
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