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<p>We study the pointwise convergence of Landau type Schrödinger operators on Bessel potential spaces <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(L_s^p (\mathbb {R})\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msubsup> <mi>L</mi> <mi>s</mi> <mi>p</mi> </msubsup> <mrow> <mo stretchy="false">(</mo> <mi mathvariant="double-struck">R</mi> <mo stretchy="false">)</mo> </mrow> </mrow> </math></EquationSource> </InlineEquation>. Our results extend those established by Bailey (Rev. Mat. Iberoam., 29 (2): 531–546, 2013) and Yuan, Zhao and Zheng (Nonlinear Anal., 208: Paper No. 112312, 28, 2021). Furthermore, we also analyze the convergence rate of Landau type Schrödinger operators along curves and derive a sharp result for the case of convergence along vertical lines.</p>

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Pointwise Convergence of Landau Type Schrödinger Operators in Bessel Potential Spaces

  • 期刊论文

  • 发表日期：

    2026年5月7日

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  • Yucheng Pan,
  • Wenchang Sun

摘要

We study the pointwise convergence of Landau type Schrödinger operators on Bessel potential spaces \(L_s^p (\mathbb {R})\) L s p ( R ) . Our results extend those established by Bailey (Rev. Mat. Iberoam., 29 (2): 531–546, 2013) and Yuan, Zhao and Zheng (Nonlinear Anal., 208: Paper No. 112312, 28, 2021). Furthermore, we also analyze the convergence rate of Landau type Schrödinger operators along curves and derive a sharp result for the case of convergence along vertical lines.