<p>This paper establishes the <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="43037_2025_460_Article_IEq1.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="20" /> </InlineMediaObject> <EquationSource Format="TEX">\(L^p\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mi>L</mi> <mi>p</mi> </msup> </math></EquationSource> </InlineEquation> boundedness of singular Radon transforms and related maximal operators associated with polynomial mappings. Compared to existing results, our approach weakens the smoothness requirement on the kernels, replacing it with a Hölder-type condition. Additionally, we relax the size and cancellation assumptions on the kernels. The bounds we obtain are uniform in the sense that they depend only on the degrees of the underlying polynomials, not on their specific coefficients.</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

Singular Radon transforms with Hölder class kernels

  • Yibiao Pan

摘要

This paper establishes the \(L^p\) L p boundedness of singular Radon transforms and related maximal operators associated with polynomial mappings. Compared to existing results, our approach weakens the smoothness requirement on the kernels, replacing it with a Hölder-type condition. Additionally, we relax the size and cancellation assumptions on the kernels. The bounds we obtain are uniform in the sense that they depend only on the degrees of the underlying polynomials, not on their specific coefficients.