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<p>We complete the <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(L^p\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mi>L</mi> <mi>p</mi> </msup> </math></EquationSource> </InlineEquation> boundedness theory of commutators of Hilbert transforms along monomial curves by providing the previously missing lower bounds. This optimal result now covers all monomial curves while the previous result assumed the curve to intersect adjacent quadrants of the plane. We also develop, under a qualitative <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(\operatorname {BMO}\)</EquationSource> <EquationSource Format="MATHML"><math> <mo>BMO</mo> </math></EquationSource> </InlineEquation> assumption of the symbol, the corresponding quantitative lower bound in the context of curves with non-vanishing torsion.</p>

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Curved commutators in the plane

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年5月20日

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  • Kangwei Li,
  • Henri Martikainen,
  • Tuomas Oikari

摘要

We complete the \(L^p\) L p boundedness theory of commutators of Hilbert transforms along monomial curves by providing the previously missing lower bounds. This optimal result now covers all monomial curves while the previous result assumed the curve to intersect adjacent quadrants of the plane. We also develop, under a qualitative \(\operatorname {BMO}\) BMO assumption of the symbol, the corresponding quantitative lower bound in the context of curves with non-vanishing torsion.