Pointwise Convergence for sequences of Schr\"{o}dinger means in $\mathbb{R}^{2}$

Wenjuan Li; Huiju Wang; Dunyan Yan

Pointwise Convergence for sequences of Schr\"{o}dinger means in $\mathbb{R}^{2}$

Classical Analysis and ODEs 2020-11-03 v2

Authors: Wenjuan Li , Huiju Wang , Dunyan Yan

Abstract

We consider pointwise convergence of Schr\"{o}dinger means $e^{it_{n}\Delta}f(x)$ for $f \in H^{s}(\mathbb{R}^{2})$ and decreasing sequences $\{t_{n}\}_{n=1}^{\infty}$ converging to zero. The main theorem improves the previous results of [Sj\"{o}lin, JFAA, 2018] and [Sj\"{o}lin-Str\"{o}mberg, JMAA, 2020] in $\mathbb{R}^{2}$ . This study is based on investigating properties of Schr\"{o}dinger type maximal functions related to hypersurfaces with vanishing Gaussian curvature.

Keywords

pointwise convergence schrödinger means maximal functions gaussian curvature harmonic analysis

Cite

@article{arxiv.2010.08701,
  title  = {Pointwise Convergence for sequences of Schr\"{o}dinger means in $\mathbb{R}^{2}$},
  author = {Wenjuan Li and Huiju Wang and Dunyan Yan},
  journal= {arXiv preprint arXiv:2010.08701},
  year   = {2020}
}

Pointwise Convergence for sequences of Schr\"{o}dinger means in $\mathbb{R}^{2}$

Abstract

Keywords

Cite

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