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<p>In this paper, we study the <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(L^{p}\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mi>L</mi> <mi>p</mi> </msup> </math></EquationSource> </InlineEquation>-improving property for the maximal operators along a large class of curves of finite type in the plane with dilation set <InlineEquation ID="IEq4"> <EquationSource Format="TEX">\(E \subset [1,2]\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>E</mi> <mo>⊂</mo> <mo stretchy="false">[</mo> <mn>1</mn> <mo>,</mo> <mn>2</mn> <mo stretchy="false">]</mo> </mrow> </math></EquationSource> </InlineEquation>. The <InlineEquation ID="IEq5"> <EquationSource Format="TEX">\(L^{p}\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mi>L</mi> <mi>p</mi> </msup> </math></EquationSource> </InlineEquation>-improving region depends on the order of finite type and the fractal dimension of <i>E</i>. In particular, various impacts of non-isotropic dilations are also considered.</p>

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On \(L^{p}\)-improving Bounds for Maximal Operators Associated with Curves of Finite Type in the Plane

  • 期刊论文

  • 发表日期：

    2026年2月18日

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  • Wenjuan Li,
  • Huiju Wang

摘要

In this paper, we study the \(L^{p}\) L p -improving property for the maximal operators along a large class of curves of finite type in the plane with dilation set \(E \subset [1,2]\) E ⊂ [ 1 , 2 ] . The \(L^{p}\) L p -improving region depends on the order of finite type and the fractal dimension of E. In particular, various impacts of non-isotropic dilations are also considered.