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<p>The aim of this paper is to give the answer to the problem of characterization of acting conditions (necessary as well as sufficient) for nonlinear composition operators in some sequence spaces. We also characterize their boundedness and local boundedness. We focus on nonlinear composition operators acting to or from the space <InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="43037_2025_429_Article_IEq3.gif" Format="GIF" Height="20" Rendition="HTML" Resolution="72" Type="Linedraw" Width="49" /> </InlineMediaObject> <EquationSource Format="TEX">\(bv_p(E)\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>b</mi> <msub> <mi>v</mi> <mi>p</mi> </msub> <mrow> <mo stretchy="false">(</mo> <mi>E</mi> <mo stretchy="false">)</mo> </mrow> </mrow> </math></EquationSource> </InlineEquation> of all sequences of <i>p</i>-bounded variation; here <InlineEquation ID="IEq4"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="43037_2025_429_Article_IEq4.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="42" /> </InlineMediaObject> <EquationSource Format="TEX">\(p\ge 1\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>p</mi> <mo>≥</mo> <mn>1</mn> </mrow> </math></EquationSource> </InlineEquation> and <i>E</i> is a normed space.</p>

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Nonlinear composition operators in \(bv_p\)-spaces: acting conditions and boundedness

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年6月10日

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  • Daria Bugajewska,
  • Piotr Kasprzak

摘要

The aim of this paper is to give the answer to the problem of characterization of acting conditions (necessary as well as sufficient) for nonlinear composition operators in some sequence spaces. We also characterize their boundedness and local boundedness. We focus on nonlinear composition operators acting to or from the space \(bv_p(E)\) b v p ( E ) of all sequences of p-bounded variation; here \(p\ge 1\) p ≥ 1 and E is a normed space.