<?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>S0120-419X2013000200004</article-id>
<title-group>
<article-title xml:lang="es"><![CDATA[Estimativos L² para una clase de operadores pseudodiferenciales definidos en el toro]]></article-title>
<article-title xml:lang="en"><![CDATA[L²-Estimates for a class of pseudo-differential operators defined on the torus]]></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="A01"/>
</contrib>
</contrib-group>
<aff id="A01">
<institution><![CDATA[,Universidad del Valle Departamento de Matemáticas ]]></institution>
<addr-line><![CDATA[Cali ]]></addr-line>
<country>Colombia</country>
</aff>
<pub-date pub-type="pub">
<day>00</day>
<month>12</month>
<year>2013</year>
</pub-date>
<pub-date pub-type="epub">
<day>00</day>
<month>12</month>
<year>2013</year>
</pub-date>
<volume>31</volume>
<numero>2</numero>
<fpage>147</fpage>
<lpage>152</lpage>
<copyright-statement/>
<copyright-year/>
<self-uri xlink:href="http://www.scielo.org.co/scielo.php?script=sci_arttext&amp;pid=S0120-419X2013000200004&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.org.co/scielo.php?script=sci_abstract&amp;pid=S0120-419X2013000200004&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.org.co/scielo.php?script=sci_pdf&amp;pid=S0120-419X2013000200004&amp;lng=en&amp;nrm=iso"></self-uri><abstract abstract-type="short" xml:lang="es"><p><![CDATA[En este trabajo se establecen estimativos L² para operadores pseudodiferenciales definidos en el toro. Los operadores considerados surgen del estudio de operadores entre grupos abelianos localmente compactos]]></p></abstract>
<abstract abstract-type="short" xml:lang="en"><p><![CDATA[In this work we establish L² estimates from pseudo-differential operators defined on the torus. Such operators arise from the study of operators on locally compact abelian groups.]]></p></abstract>
<kwd-group>
<kwd lng="es"><![CDATA[Operadores pseudo-diferenciales]]></kwd>
<kwd lng="es"><![CDATA[continuidad en L²]]></kwd>
<kwd lng="es"><![CDATA[grupos localmente compactos]]></kwd>
<kwd lng="en"><![CDATA[Pseudo-differential operators]]></kwd>
<kwd lng="en"><![CDATA[L²-boundedness]]></kwd>
<kwd lng="en"><![CDATA[locally compact groups]]></kwd>
</kwd-group>
</article-meta>
</front><body><![CDATA[   <font size="2" face="Verdana">     <p align="center"><font size="4"><b><i>Estimativos L<sup>2</sup> para una clase de operadores    <br> pseudodiferenciales definidos en el toro</i></b></font></p>      <p align="center">DUV&Aacute;N CARDONA<sup>*</sup>    <br>     <P align="center">Universidad del Valle, Departamento de Matem&aacute;ticas, A.A 25360, Cali, Colombia.</P> <hr>     <p align="justify"><b><i>Resumen</i></b>. En este trabajo se establecen estimativos L<sup>2</sup> para operadores pseudodiferenciales definidos en el toro. Los operadores considerados surgen del estudio de operadores entre grupos abelianos localmente compactos.    <br> <b><i>Palabras claves</i></b>: Operadores pseudo-diferenciales, continuidad en L<sup>2</sup>, grupos localmente compactos.    <br> <b><i>MSC2010</i></b>: 47G30, 65R10.</p> <hr>     <p align="center"><font size="3"><b><i>L<sup>2</sup>-Estimates for a class of pseudo-differential operators defined on the torus</i></b></font></p>      ]]></body>
<body><![CDATA[<p align="justify"><b><i>Abstract</i></b>. In this work we establish L<sup>2</sup> estimates from pseudo-differential operators defined on the torus. Such operators arise from the study of operators on locally compact abelian groups.    <br> <b><i>Keywords:</i></b> Pseudo-differential operators, L<sup>2</sup>-boundedness, locally compact groups.</p> <hr>     <p align="justify">Texto Completo disponible en <a href ="pdf\rein\v31n2\v31n2a04.pdf">PDF</a></p> <hr>      <p align="left"><font size="3"><b><i>Referencias</i></b></font></p>      <!-- ref --><p align="justify">&#91;1&#93; Agranovich M.S., &quot;Spectral properties of elliptic pseudo-differential operators on a closed curve&quot;, <i>Funct. Anal. Appl</i>. 13 (1979), 279-281.    &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;[&#160;<a href="javascript:void(0);" onclick="javascript: window.open('/scielo.php?script=sci_nlinks&ref=000017&pid=S0120-419X201300020000400001&lng=','','width=640,height=500,resizable=yes,scrollbars=1,menubar=yes,');">Links</a>&#160;]<!-- end-ref --></p>      <!-- ref --><p align="justify">&#91;2&#93; Ashino R., Nagase M., and Vaillancourt R., &quot;Pseudo-differential Operators on <i>L<sup>p</sup> spaces&quot;, Cubo</i> 6 (2004), no. 3, 91-129.    &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;[&#160;<a href="javascript:void(0);" onclick="javascript: window.open('/scielo.php?script=sci_nlinks&ref=000019&pid=S0120-419X201300020000400002&lng=','','width=640,height=500,resizable=yes,scrollbars=1,menubar=yes,');">Links</a>&#160;]<!-- end-ref --></p>      <!-- ref --><p align="justify">&#91;3&#93; Calder&oacute;n A. and Vaillancourt R., &quot;On the boundedness of pseudo-differential operators&quot;, <i>J. Math. Soc. Japan</i> 23 (1971), 374-378.    &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;[&#160;<a href="javascript:void(0);" onclick="javascript: window.open('/scielo.php?script=sci_nlinks&ref=000021&pid=S0120-419X201300020000400003&lng=','','width=640,height=500,resizable=yes,scrollbars=1,menubar=yes,');">Links</a>&#160;]<!-- end-ref --></p>      ]]></body>
<body><![CDATA[<!-- ref --><p align="justify">&#91;4&#93; Delgado J., &quot;Lp bounds for pseudo-differential operators defined on the torus&quot;, <i>Operators Theory: Advances and Applications</i> 231 (2013), 103-116.    &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;[&#160;<a href="javascript:void(0);" onclick="javascript: window.open('/scielo.php?script=sci_nlinks&ref=000023&pid=S0120-419X201300020000400004&lng=','','width=640,height=500,resizable=yes,scrollbars=1,menubar=yes,');">Links</a>&#160;]<!-- end-ref --></p>      <!-- ref --><p align="justify">&#91;5&#93; Molahajloo S. and Wong M.W., &quot;Pseudo-Differential operators on S<sup>1</sup>&quot;, in <i>New developments on Pseudo-Differential operators</i>, Eds. Luigi Rodino and M.W. Wong. (2008), 297-306.    &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;[&#160;<a href="javascript:void(0);" onclick="javascript: window.open('/scielo.php?script=sci_nlinks&ref=000025&pid=S0120-419X201300020000400005&lng=','','width=640,height=500,resizable=yes,scrollbars=1,menubar=yes,');">Links</a>&#160;]<!-- end-ref --></p>      <!-- ref --><p align="justify">&#91;6&#93; Ruzhansky M. and Turunen V., <i>Pseudo-differential Operators and Symmetries: Background Analysis and Advanced Topics</i>, Birkha&uuml;ser-Verlag, Basel, 2010.    &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;[&#160;<a href="javascript:void(0);" onclick="javascript: window.open('/scielo.php?script=sci_nlinks&ref=000027&pid=S0120-419X201300020000400006&lng=','','width=640,height=500,resizable=yes,scrollbars=1,menubar=yes,');">Links</a>&#160;]<!-- end-ref --></p>      <!-- ref --><p align="justify">&#91;7&#93; Ruzhansky M. and Turunen V., &quot;Quantization of Pseudo-Differential Operators on the Torus&quot;, <i>J. Fourier Annal Appl</i>. 16 (2010), 943-982.    &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;[&#160;<a href="javascript:void(0);" onclick="javascript: window.open('/scielo.php?script=sci_nlinks&ref=000029&pid=S0120-419X201300020000400007&lng=','','width=640,height=500,resizable=yes,scrollbars=1,menubar=yes,');">Links</a>&#160;]<!-- end-ref --></p>      <!-- ref --><p align="justify">&#91;8&#93; Taylor M., &quot;Pseudodifferential Operators&quot;, <i>Four Lectures at MSRI</i>, September 2008, p. 16.    &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;[&#160;<a href="javascript:void(0);" onclick="javascript: window.open('/scielo.php?script=sci_nlinks&ref=000031&pid=S0120-419X201300020000400008&lng=','','width=640,height=500,resizable=yes,scrollbars=1,menubar=yes,');">Links</a>&#160;]<!-- end-ref --></p>      ]]></body>
<body><![CDATA[<!-- ref --><p align="justify">&#91;9&#93; Wong M.W., &quot;Discrete Fourier Analysis&quot;, Birkha&uuml;ser: Germany, 2011.    &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;[&#160;<a href="javascript:void(0);" onclick="javascript: window.open('/scielo.php?script=sci_nlinks&ref=000033&pid=S0120-419X201300020000400009&lng=','','width=640,height=500,resizable=yes,scrollbars=1,menubar=yes,');">Links</a>&#160;]<!-- end-ref --></p> </font>     <blockquote><font size="2" face="Verdana">   <hr>    </font></blockquote> <font size="2" face="Verdana">     <p align="justify"><sup>*</sup><i>E-mail:</i> <a href="mailto:duvanc306@gmail.com">duvanc306@gmail.com</a>    <br> Recibido: 20 de agosto de 2013, Aceptado: 19 de noviembre de 2013.</p> </font>      ]]></body><back>
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