On the rate of convergence for Landau type Schr\"odinger Operators

TL;DR

This paper investigates the pointwise convergence and convergence rates of Landau type Schr"odinger operators in fractional Sobolev spaces, extending previous results and analyzing convergence along curves and vertical lines.

Contribution

It extends existing convergence results for Landau type Schr"odinger operators to fractional Sobolev spaces and provides sharp convergence rate estimates along specific curves.

Findings

Extended convergence results to fractional Sobolev spaces.

Derived sharp convergence rate estimates along curves.

Analyzed convergence along vertical lines.

Abstract

We study the pointwise convergence of Landau type Schr\"odinger operators within the fractional Sobolev space $W^{s,p}(\mathbb R)$. 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 Schr\"odinger operators along curves and derive a sharp result for the case of convergence along vertical lines.