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<p>In this paper, we consider convergence properties for generalized Schrödinger operators along tangential curves in ℝ<sup><i>n</i></sup> × ℝ with less smoothness comparing with Lipschitz condition. Firstly, we obtain sharp convergence rate for generalized Schrödinger operators with polynomial growth along tangential curves in ℝ<sup><i>n</i></sup> × ℝ, <i>n</i> ≥ 1. Secondly, we get the convergence result along a family of restricted tangential curves in ℝ × ℝ. As a corollary, we obtain the sharp <i>L</i><sup><i>p</i></sup>-Schrödinger maximal estimates along tangential curves in ℝ × ℝ.</p>

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On convergence properties for generalized Schrödinger operators along tangential curves

  • 期刊论文

  • 发表日期：

    2025年12月22日

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  • Huiju Wang,
  • Wenjuan Li

摘要

In this paper, we consider convergence properties for generalized Schrödinger operators along tangential curves in ℝn × ℝ with less smoothness comparing with Lipschitz condition. Firstly, we obtain sharp convergence rate for generalized Schrödinger operators with polynomial growth along tangential curves in ℝn × ℝ, n ≥ 1. Secondly, we get the convergence result along a family of restricted tangential curves in ℝ × ℝ. As a corollary, we obtain the sharp Lp-Schrödinger maximal estimates along tangential curves in ℝ × ℝ.