On the rate of convergence for Landau type Schrödinger Operators

Abstract

We study the pointwise convergence of Landau type Schrödinger 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 Schrödinger operators along curves and derive a sharp result for the case of convergence along vertical lines.

23 pages