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<p>In this paper, we present a survey of some recent results on estimates for Green’s operators and some Sobolev-type inequalities with respect to the de Rham operator <i>d</i>, the Laplacian <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\varDelta \)</EquationSource> <EquationSource Format="MATHML"><math> <mi>Δ</mi> </math></EquationSource> </InlineEquation>, and the operator <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(\bar{\partial }\)</EquationSource> <EquationSource Format="MATHML"><math> <mover accent="true"> <mrow> <mi>∂</mi> </mrow> <mrow> <mo stretchy="false">¯</mo> </mrow> </mover> </math></EquationSource> </InlineEquation> for functions or twisted differential forms on real and complex manifolds.</p>

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A survey on estimates of Green’s operator and Sobolev-type inequalities

  • 期刊论文

  • 发表日期：

    2025年12月11日

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  • Fusheng Deng,
  • Gang Huang,
  • Xiangsen Qin

摘要

In this paper, we present a survey of some recent results on estimates for Green’s operators and some Sobolev-type inequalities with respect to the de Rham operator d, the Laplacian \(\varDelta \) Δ , and the operator \(\bar{\partial }\) ∂ ¯ for functions or twisted differential forms on real and complex manifolds.