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<p>In this paper we study some properties of the space <InlineEquation ID="IEq6"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="13370_2025_1280_Article_IEq6.gif" Format="GIF" Height="24" Rendition="HTML" Resolution="72" Type="Linedraw" Width="109" /> </InlineMediaObject> <EquationSource Format="TEX">\(RBV_{(p,\alpha )}^{0}([a,b])\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>R</mi> <mi>B</mi> <msubsup> <mi>V</mi> <mrow> <mo stretchy="false">(</mo> <mi>p</mi> <mo>,</mo> <mi>α</mi> <mo stretchy="false">)</mo> </mrow> <mn>0</mn> </msubsup> <mrow> <mo stretchy="false">(</mo> <mrow> <mo stretchy="false">[</mo> <mi>a</mi> <mo>,</mo> <mi>b</mi> <mo stretchy="false">]</mo> </mrow> <mo stretchy="false">)</mo> </mrow> </mrow> </math></EquationSource> </InlineEquation>. Among other, we proved that the dual space of <InlineEquation ID="IEq7"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="13370_2025_1280_Article_IEq7.gif" Format="GIF" Height="21" Rendition="HTML" Resolution="72" Type="Linedraw" Width="84" /> </InlineMediaObject> <EquationSource Format="TEX">\(L_{(p,\alpha )}([a,b])\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msub> <mi>L</mi> <mrow> <mo stretchy="false">(</mo> <mi>p</mi> <mo>,</mo> <mi>α</mi> <mo stretchy="false">)</mo> </mrow> </msub> <mrow> <mo stretchy="false">(</mo> <mrow> <mo stretchy="false">[</mo> <mi>a</mi> <mo>,</mo> <mi>b</mi> <mo stretchy="false">]</mo> </mrow> <mo stretchy="false">)</mo> </mrow> </mrow> </math></EquationSource> </InlineEquation> may be identified with the space <InlineEquation ID="IEq8"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="13370_2025_1280_Article_IEq6.gif" Format="GIF" Height="24" Rendition="HTML" Resolution="72" Type="Linedraw" Width="109" /> </InlineMediaObject> <EquationSource Format="TEX">\(RBV_{(p,\alpha )}^{0}([a,b])\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>R</mi> <mi>B</mi> <msubsup> <mi>V</mi> <mrow> <mo stretchy="false">(</mo> <mi>p</mi> <mo>,</mo> <mi>α</mi> <mo stretchy="false">)</mo> </mrow> <mn>0</mn> </msubsup> <mrow> <mo stretchy="false">(</mo> <mrow> <mo stretchy="false">[</mo> <mi>a</mi> <mo>,</mo> <mi>b</mi> <mo stretchy="false">]</mo> </mrow> <mo stretchy="false">)</mo> </mrow> </mrow> </math></EquationSource> </InlineEquation>.</p>

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On the \(\mathbf {RBV_{(p,\alpha )}^{0}([a,b])}\) variation space as the dual space of \(\mathbf {L_{(p,\alpha )}([a,b])}\)

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  • 发表日期：

    2025年4月7日

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  • René Erlin Castillo,
  • Eduard Trousselot

摘要

In this paper we study some properties of the space \(RBV_{(p,\alpha )}^{0}([a,b])\) R B V ( p , α ) 0 ( [ a , b ] ) . Among other, we proved that the dual space of \(L_{(p,\alpha )}([a,b])\) L ( p , α ) ( [ a , b ] ) may be identified with the space \(RBV_{(p,\alpha )}^{0}([a,b])\) R B V ( p , α ) 0 ( [ a , b ] ) .