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<p>We prove subelliptic estimates for the complex Green operator <InlineEquation ID="IEq4"> <EquationSource Format="TEX">\( K_q \)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>K</mi> <mi>q</mi> </msub> </math></EquationSource> </InlineEquation> at a specific level <i>q</i> of the <InlineEquation ID="IEq5"> <EquationSource Format="TEX">\( \bar{\partial }_b\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mover accent="true"> <mrow> <mi>∂</mi> </mrow> <mrow> <mo stretchy="false">¯</mo> </mrow> </mover> <mi>b</mi> </msub> </math></EquationSource> </InlineEquation>-complex, defined on a not necessarily pseudoconvex CR manifold satisfying the commutator finite type condition. Additionally, we obtain maximal <InlineEquation ID="IEq6"> <EquationSource Format="TEX">\( L^p \)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mi>L</mi> <mi>p</mi> </msup> </math></EquationSource> </InlineEquation> estimates for <InlineEquation ID="IEq7"> <EquationSource Format="TEX">\( K_q \)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>K</mi> <mi>q</mi> </msub> </math></EquationSource> </InlineEquation> by considering closed-range estimates. Our results apply to a family of manifolds that includes a class of weak <i>Y</i>(<i>q</i>) manifolds satisfying the condition <i>D</i>(<i>q</i>) . We employ a microlocal decomposition and Calderon-Zygmund theory to obtain subelliptic and maximal-<InlineEquation ID="IEq8"> <EquationSource Format="TEX">\( L^p \)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mi>L</mi> <mi>p</mi> </msup> </math></EquationSource> </InlineEquation> estimates, respectively.</p>

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Subelliptic and Maximal \( L^p \) Estimates for the Complex Green Operator on Non-pseudoconvex Domains

  • 期刊论文

  • 发表日期：

    2026年3月19日

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  • Joel Coacalle

摘要

We prove subelliptic estimates for the complex Green operator \( K_q \) K q at a specific level q of the \( \bar{\partial }_b\) ∂ ¯ b -complex, defined on a not necessarily pseudoconvex CR manifold satisfying the commutator finite type condition. Additionally, we obtain maximal \( L^p \) L p estimates for \( K_q \) K q by considering closed-range estimates. Our results apply to a family of manifolds that includes a class of weak Y(q) manifolds satisfying the condition D(q) . We employ a microlocal decomposition and Calderon-Zygmund theory to obtain subelliptic and maximal- \( L^p \) L p estimates, respectively.