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<p>In this work we obtain boundedness results for the fractional integral operator of the the bi-harmonic Schrödinger operator on weighted Lebesgue and BMO type spaces in <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="41_2025_10150_Article_IEq1.gif" Format="GIF" Height="17" Rendition="HTML" Resolution="72" Type="Linedraw" Width="20" /> </InlineMediaObject> <EquationSource Format="TEX">\(\mathbb {R}^d\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mrow> <mi mathvariant="double-struck">R</mi> </mrow> <mi>d</mi> </msup> </math></EquationSource> </InlineEquation> with <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="41_2025_10150_Article_IEq2.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="41" /> </InlineMediaObject> <EquationSource Format="TEX">\(d\ge 5\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>d</mi> <mo>≥</mo> <mn>5</mn> </mrow> </math></EquationSource> </InlineEquation>. The techniques are based on some new estimates involving the kernel of the heat semigroup.</p>

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Boundedness for Fractional Integral of the Bi-Harmonic Schrödinger Operator

  • 期刊论文

  • 发表日期：

    2025年3月26日

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  • Bruno Bongioanni,
  • Marisa Toschi,
  • Bruno Urrutia

摘要

In this work we obtain boundedness results for the fractional integral operator of the the bi-harmonic Schrödinger operator on weighted Lebesgue and BMO type spaces in \(\mathbb {R}^d\) R d with \(d\ge 5\) d ≥ 5 . The techniques are based on some new estimates involving the kernel of the heat semigroup.