#### Vol. 273, No. 1, 2015

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Maximal estimates for Schrödinger equations with inverse-square potential

### Changxing Miao, Junyong Zhang and Jiqiang Zheng

Vol. 273 (2015), No. 1, 1–19
##### Abstract

We consider maximal estimates for the solution to an initial value problem of the linear Schrödinger equation with a singular potential. We show a result about the pointwise convergence of solutions to this special variable coefficient Schrödinger equation with initial data ${u}_{0}\in {H}^{s}\left({ℝ}^{n}\right)$ for $s>\frac{1}{2}$ or radial initial data ${u}_{0}\in {H}^{s}\left({ℝ}^{n}\right)$ for $s\ge \frac{1}{4}$ and that the solution does not converge when $s<\frac{1}{4}$.

##### Keywords
inverse square potential, maximal estimate, spherical harmonics
##### Mathematical Subject Classification 2010
Primary: 35B65, 35Q55, 47J35