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<p>It is known that the pseudodifferential operator is an important tool to study hypo-elliptic equations. The known results include the continuity properties of pseudodifferential operators on local Hardy spaces <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11868_2025_689_Article_IEq1.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="19" /> </InlineMediaObject> <EquationSource Format="TEX">\(h^{p}\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mi>h</mi> <mi>p</mi> </msup> </math></EquationSource> </InlineEquation> for <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11868_2025_689_Article_IEq2.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="83" /> </InlineMediaObject> <EquationSource Format="TEX">\(0&lt;p&lt;\infty \)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mn>0</mn> <mo>&lt;</mo> <mi>p</mi> <mo>&lt;</mo> <mi>∞</mi> </mrow> </math></EquationSource> </InlineEquation> and its dual spaces. In this paper, using the calculus of symbols, we generalize existing results in one-parameter setting to multi-parameter case.</p>

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Continuity properties of multi-parameter pseudodifferential operators via calculus of symbols

  • 期刊论文

  • 发表日期：

    2025年4月3日

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  • Wei Ding,
  • Tianyu Zhang,
  • Yueping Zhu

摘要

It is known that the pseudodifferential operator is an important tool to study hypo-elliptic equations. The known results include the continuity properties of pseudodifferential operators on local Hardy spaces \(h^{p}\) h p for \(0<p<\infty \) 0 < p < ∞ and its dual spaces. In this paper, using the calculus of symbols, we generalize existing results in one-parameter setting to multi-parameter case.