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<p>We characterize the geometrically doubling condition of a metric space in terms of the uniform <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10476_2025_68_Article_IEq1.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="19" /> </InlineMediaObject> <EquationSource Format="TEX">\(L^1\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mi>L</mi> <mn>1</mn> </msup> </math></EquationSource> </InlineEquation>-boundedness of superaveraging operators, where uniform refers to the existence of bounds independent of the measure being considered.</p>

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Boundedness properties of modified averaging operators and geometrically doubling metric spaces

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年2月26日

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  • J. M. Aldaz,
  • A. Caldera

摘要

We characterize the geometrically doubling condition of a metric space in terms of the uniform \(L^1\) L 1 -boundedness of superaveraging operators, where uniform refers to the existence of bounds independent of the measure being considered.