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<p>This note establishes a conjecture of E.M.&#xa0;Stein for atoms on the Heisenberg group associated to the natural flag structure: the basic components of the atoms are convolutions of atoms for the Folland–Stein–Christ–Geller Hardy space <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="12220_2025_2207_Article_IEq1.gif" Format="GIF" Height="20" Rendition="HTML" Resolution="72" Type="Linedraw" Width="55" /> </InlineMediaObject> <EquationSource Format="TEX">\(H^1(\mathbb {H}^n)\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msup> <mi>H</mi> <mn>1</mn> </msup> <mrow> <mo stretchy="false">(</mo> <msup> <mrow> <mi mathvariant="double-struck">H</mi> </mrow> <mi>n</mi> </msup> <mo stretchy="false">)</mo> </mrow> </mrow> </math></EquationSource> </InlineEquation> and atoms for the classical Hardy space <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="12220_2025_2207_Article_IEq2.gif" Format="GIF" Height="20" Rendition="HTML" Resolution="72" Type="Linedraw" Width="46" /> </InlineMediaObject> <EquationSource Format="TEX">\(H^1(\mathbb {R})\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msup> <mi>H</mi> <mn>1</mn> </msup> <mrow> <mo stretchy="false">(</mo> <mi mathvariant="double-struck">R</mi> <mo stretchy="false">)</mo> </mrow> </mrow> </math></EquationSource> </InlineEquation> in the central variable.</p>

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Flag Hardy Spaces and Partial Differential Equations

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年9月27日

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  • Michael G. Cowling,
  • Ji Li

摘要

This note establishes a conjecture of E.M. Stein for atoms on the Heisenberg group associated to the natural flag structure: the basic components of the atoms are convolutions of atoms for the Folland–Stein–Christ–Geller Hardy space \(H^1(\mathbb {H}^n)\) H 1 ( H n ) and atoms for the classical Hardy space \(H^1(\mathbb {R})\) H 1 ( R ) in the central variable.