<?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>S0120-419X2017000200215</article-id>
<article-id pub-id-type="doi">10.18273/revint.v35n2-2017005</article-id>
<title-group>
<article-title xml:lang="en"><![CDATA[Approximation properties on Herz spaces]]></article-title>
<article-title xml:lang="es"><![CDATA[Propiedades de aproximación en espacios de Herz]]></article-title>
</title-group>
<contrib-group>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Pérez-López]]></surname>
<given-names><![CDATA[Jhean E.]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
</contrib-group>
<aff id="Af1">
<institution><![CDATA[,Universidad Industrial de Santander  ]]></institution>
<addr-line><![CDATA[ ]]></addr-line>
<country>Colombia</country>
</aff>
<pub-date pub-type="pub">
<day>00</day>
<month>12</month>
<year>2017</year>
</pub-date>
<pub-date pub-type="epub">
<day>00</day>
<month>12</month>
<year>2017</year>
</pub-date>
<volume>35</volume>
<numero>2</numero>
<fpage>215</fpage>
<lpage>223</lpage>
<copyright-statement/>
<copyright-year/>
<self-uri xlink:href="http://www.scielo.org.co/scielo.php?script=sci_arttext&amp;pid=S0120-419X2017000200215&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.org.co/scielo.php?script=sci_abstract&amp;pid=S0120-419X2017000200215&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.org.co/scielo.php?script=sci_pdf&amp;pid=S0120-419X2017000200215&amp;lng=en&amp;nrm=iso"></self-uri><abstract abstract-type="short" xml:lang="en"><p><![CDATA[Abstract  In this paper we consider the Herz spaces K&#945; p,q, which are a natural generalization of the Lebesgue spaces Lp. We prove some approximation properties such as density of the space C &#8734;  c (R n), continuity of the translation, continuity of the mollification, global behavior of the convolution with smooth functions, among others.  MSC2010: 26B05, 26B35, 26B99.]]></p></abstract>
<abstract abstract-type="short" xml:lang="es"><p><![CDATA[Resumen  En este artículo consideramos los espacios de Herz K&#945; p,q, los cuales son una generalización natural de los espacios de Lebesgue Lp. Demostramos algunas propiedades de aproximación tal es como densidad del espacio C &#8734;  c (R n), continuidad de la traslación, continuidad de la molificación, comportamiento global de la convolución con funciones suaves, entre otras.]]></p></abstract>
<kwd-group>
<kwd lng="en"><![CDATA[Herz spaces]]></kwd>
<kwd lng="en"><![CDATA[Mollifiers]]></kwd>
<kwd lng="en"><![CDATA[Convolution]]></kwd>
<kwd lng="en"><![CDATA[Functional spaces]]></kwd>
<kwd lng="es"><![CDATA[Espacios de Herz]]></kwd>
<kwd lng="es"><![CDATA[Molificadores]]></kwd>
<kwd lng="es"><![CDATA[Convolución]]></kwd>
<kwd lng="es"><![CDATA[Espacios funcionales]]></kwd>
</kwd-group>
</article-meta>
</front><back>
<ref-list>
<ref id="B1">
<label>[1]</label><nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Chen]]></surname>
<given-names><![CDATA[Y.Z.]]></given-names>
</name>
<name>
<surname><![CDATA[Lau]]></surname>
<given-names><![CDATA[K.S.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[On some new classes of Hardy spaces]]></article-title>
<source><![CDATA[J. Funct. Anal.]]></source>
<year>1989</year>
<volume>84</volume>
<page-range>255-78</page-range></nlm-citation>
</ref>
<ref id="B2">
<label>[2]</label><nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[DiPerna]]></surname>
<given-names><![CDATA[R.J.]]></given-names>
</name>
<name>
<surname><![CDATA[Lions]]></surname>
<given-names><![CDATA[P.L.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Ordinary differential equations, transport theory and Sobolev spaces]]></article-title>
<source><![CDATA[Invent. Math.]]></source>
<year>1989</year>
<volume>98</volume>
<numero>3</numero>
<issue>3</issue>
<page-range>511-47</page-range></nlm-citation>
</ref>
<ref id="B3">
<label>[3]</label><nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Ferreira]]></surname>
<given-names><![CDATA[L.C.F.]]></given-names>
</name>
<name>
<surname><![CDATA[Pérez-López]]></surname>
<given-names><![CDATA[J.E.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[On the theory of Besov&#8211;Herz spaces and Euler equations]]></article-title>
<source><![CDATA[Israel J. Math.]]></source>
<year>2017</year>
<volume>220</volume>
<numero>1</numero>
<issue>1</issue>
<page-range>283-332</page-range></nlm-citation>
</ref>
<ref id="B4">
<label>[4]</label><nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[García-Cuerva]]></surname>
<given-names><![CDATA[J.]]></given-names>
</name>
<name>
<surname><![CDATA[Herrero]]></surname>
<given-names><![CDATA[M.-J.L.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[A theory of Hardy spaces associated to the Herz spaces]]></article-title>
<source><![CDATA[Proc. Lond. Math. Soc.]]></source>
<year>1994</year>
<volume>69</volume>
<numero>3</numero>
<issue>3</issue>
<page-range>605-28</page-range></nlm-citation>
</ref>
<ref id="B5">
<label>[5]</label><nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Grafakos]]></surname>
<given-names><![CDATA[L.]]></given-names>
</name>
<name>
<surname><![CDATA[Li]]></surname>
<given-names><![CDATA[X.]]></given-names>
</name>
<name>
<surname><![CDATA[Yang]]></surname>
<given-names><![CDATA[D.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Bilinear Operators on Herz-type Hardy spaces]]></article-title>
<source><![CDATA[Trans. Amer. Math. Soc.]]></source>
<year>1998</year>
<volume>350</volume>
<numero>3</numero>
<issue>3</issue>
<page-range>1249-75</page-range></nlm-citation>
</ref>
<ref id="B6">
<label>[6]</label><nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Hernandez]]></surname>
<given-names><![CDATA[E.]]></given-names>
</name>
<name>
<surname><![CDATA[Yang]]></surname>
<given-names><![CDATA[D.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Interpolation of Herz spaces and applications]]></article-title>
<source><![CDATA[Math. Nachr.]]></source>
<year>1999</year>
<volume>205</volume>
<numero>1</numero>
<issue>1</issue>
<page-range>69-87</page-range></nlm-citation>
</ref>
<ref id="B7">
<label>[7]</label><nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Herz]]></surname>
<given-names><![CDATA[C.S.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Lipschitz spaces and Bernstein&#8217;s theorem on absolutely convergent Fourier transforms]]></article-title>
<source><![CDATA[J. Math. Mech.]]></source>
<year>1969</year>
<volume>18</volume>
<page-range>283-323</page-range></nlm-citation>
</ref>
<ref id="B8">
<label>[8]</label><nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Johnson]]></surname>
<given-names><![CDATA[R.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Lipschitz spaces, Littlewood-Paley spaces, and convoluteurs]]></article-title>
<source><![CDATA[Proc. Lond. Math. Soc.]]></source>
<year>1974</year>
<volume>29</volume>
<numero>1</numero>
<issue>1</issue>
<page-range>127-41</page-range></nlm-citation>
</ref>
<ref id="B9">
<label>[9]</label><nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Tsutsui]]></surname>
<given-names><![CDATA[Y.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[The Navier-Stokes equations and weak Herz spaces]]></article-title>
<source><![CDATA[Adv. Differential Equations]]></source>
<year>2011</year>
<volume>16</volume>
<numero>11-12</numero>
<issue>11-12</issue>
<page-range>1049-85</page-range></nlm-citation>
</ref>
<ref id="B10">
<label>[10]</label><nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Xu]]></surname>
<given-names><![CDATA[J.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Equivalent norms of Herz-type Besov and Triebel-Lizorkin spaces]]></article-title>
<source><![CDATA[J. Funct. Spaces Appl.]]></source>
<year>2005</year>
<volume>3</volume>
<numero>1</numero>
<issue>1</issue>
<page-range>17-31</page-range></nlm-citation>
</ref>
</ref-list>
</back>
</article>
