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<p>In this article, we focus on the construction of multivariate fractal functions in Lebesgue spaces along with some properties of associated fractal operator. First, we give a detailed construction of the fractal functions belonging to Lebesgue spaces. Then, we give analytical properties of the defined fractal operator in Lebesgue spaces. We end this article by showing the existence of Schauder basis of the associated fractal functions for the space <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="40065_2025_555_Article_IEq1.gif" Format="GIF" Height="20" Rendition="HTML" Resolution="72" Type="Linedraw" Width="72" /> </InlineMediaObject> <EquationSource Format="TEX">\(\mathcal {L}^q(I^n, \mu _p)\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msup> <mrow> <mi mathvariant="script">L</mi> </mrow> <mi>q</mi> </msup> <mrow> <mo stretchy="false">(</mo> <msup> <mi>I</mi> <mi>n</mi> </msup> <mo>,</mo> <msub> <mi>μ</mi> <mi>p</mi> </msub> <mo stretchy="false">)</mo> </mrow> </mrow> </math></EquationSource> </InlineEquation>.</p>

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Some analytical properties of multivariate fractal functions in Lebesgue spaces

  • 期刊论文

  • 发表日期：

    2025年8月14日

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  • Kiran Rani,
  • Rattan Lal

摘要

In this article, we focus on the construction of multivariate fractal functions in Lebesgue spaces along with some properties of associated fractal operator. First, we give a detailed construction of the fractal functions belonging to Lebesgue spaces. Then, we give analytical properties of the defined fractal operator in Lebesgue spaces. We end this article by showing the existence of Schauder basis of the associated fractal functions for the space \(\mathcal {L}^q(I^n, \mu _p)\) L q ( I n , μ p ) .