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<p>A new upper bound for the maximal function of Schrödinger is obtained in <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="43037_2025_428_Article_IEq1.gif" Format="GIF" Height="22" Rendition="HTML" Resolution="72" Type="Linedraw" Width="46" /> </InlineMediaObject> <EquationSource Format="TEX">\(L^{\frac{2(n+1)}{n}}\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mi>L</mi> <mfrac> <mrow> <mn>2</mn> <mo stretchy="false">(</mo> <mi>n</mi> <mo>+</mo> <mn>1</mn> <mo stretchy="false">)</mo> </mrow> <mi>n</mi> </mfrac> </msup> </math></EquationSource> </InlineEquation> by establishing weighted estimates. The main ingredients are the polynomial partitioning, and induction on the scales and the dimensions of varieties. As an application, the index region of the local space-time estimates for Schrödinger equation is extended when <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="43037_2025_428_Article_IEq2.gif" Format="GIF" Height="15" Rendition="HTML" Resolution="72" Type="Linedraw" Width="79" /> </InlineMediaObject> <EquationSource Format="TEX">\(3\le n\le 5.\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mn>3</mn> <mo>≤</mo> <mi>n</mi> <mo>≤</mo> <mn>5</mn> <mo>.</mo> </mrow> </math></EquationSource> </InlineEquation></p>

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An upper bound on the maximal function of Schrödinger operator

  • 期刊论文

  • 发表日期：

    2025年5月2日

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  • Junfeng Li,
  • Ankang Yu

摘要

A new upper bound for the maximal function of Schrödinger is obtained in \(L^{\frac{2(n+1)}{n}}\) L 2 ( n + 1 ) n by establishing weighted estimates. The main ingredients are the polynomial partitioning, and induction on the scales and the dimensions of varieties. As an application, the index region of the local space-time estimates for Schrödinger equation is extended when \(3\le n\le 5.\) 3 ≤ n ≤ 5 .