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<p>In this work we obtain weighted boundedness results for singular integral operators with kernels exhibiting exponential decay. We also show that the classes of weights are characterized by a suitable maximal operator. Additionally, we study the boundedness of various operators associated with the generalized Schrödinger operator <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(-\Delta + \mu \)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mo>-</mo> <mi mathvariant="normal">Δ</mi> <mo>+</mo> <mi>μ</mi> </mrow> </math></EquationSource> </InlineEquation>, where <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(\mu \)</EquationSource> <EquationSource Format="MATHML"><math> <mi>μ</mi> </math></EquationSource> </InlineEquation> is a nonnegative Radon measure in <InlineEquation ID="IEq3"> <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>, for&#xa0;<InlineEquation ID="IEq4"> <EquationSource Format="TEX">\({d\ge 3}.\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mrow> <mi>d</mi> <mo>≥</mo> <mn>3</mn> </mrow> <mo>.</mo> </mrow> </math></EquationSource> </InlineEquation></p>

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Weighted estimates for Schrödinger–Calderón–Zygmund operators with exponential decay

  • 期刊论文

  • 发表日期：

    2025年10月24日

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  • Estefanía Dalmasso,
  • Gabriela R. Lezama,
  • Marisa Toschi

摘要

In this work we obtain weighted boundedness results for singular integral operators with kernels exhibiting exponential decay. We also show that the classes of weights are characterized by a suitable maximal operator. Additionally, we study the boundedness of various operators associated with the generalized Schrödinger operator \(-\Delta + \mu \) - Δ + μ , where \(\mu \) μ is a nonnegative Radon measure in \(\mathbb {R}^d\) R d , for  \({d\ge 3}.\) d ≥ 3 .