Scholarlink

Abstract <p>We consider maximal operators associated with a class of parameterized singular hypersurfaces in <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="12202_2025_8250_Article_IEq1.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="40" /> </InlineMediaObject> <EquationSource Format="TEX">\(\mathbb{R}^{n+1},\)</EquationSource> <!--LobJMat2560523Usmanov-m1--> </InlineEquation> showing boundedness of these operators in Lebesgue <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="12202_2025_8250_Article_IEq2.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="20" /> </InlineMediaObject> <EquationSource Format="TEX">\(L^{p}\)</EquationSource> <!--LobJMat2560523Usmanov-m2--> </InlineEquation> space for <InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="12202_2025_8250_Article_IEq3.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="42" /> </InlineMediaObject> <EquationSource Format="TEX">\(p&gt;2\)</EquationSource> <!--LobJMat2560523Usmanov-m3--> </InlineEquation>. Also, we prove that at least one of the principal curvatures is non-zero at each regular point of these hypersurfaces.</p>

错误：搜索内容不能为空，请输入英文关键词
错误：关键词超出字数限制，请精简
高级检索

Maximal Averages over Singular Hypersurfaces

  • 期刊论文

  • 发表日期：

    2025年3月1日

查看全文
  • Salim Usmanov,
  • Ismail Ekincioglu

摘要

Abstract

We consider maximal operators associated with a class of parameterized singular hypersurfaces in \(\mathbb{R}^{n+1},\) showing boundedness of these operators in Lebesgue \(L^{p}\) space for \(p>2\) . Also, we prove that at least one of the principal curvatures is non-zero at each regular point of these hypersurfaces.