Pointwise convergence of sequential Schrödinger means

Abstract We study pointwise convergence of the fractional Schrödinger means along sequences $t_{n}$ t n that converge to zero. Our main result is bounds on maximal function $\sup_{n} |e^{it_{n}(-\Delta )^{\alpha /2}} f| $ sup | e i ( − Δ ) α / 2 f can be deduced from those $\sup_{0< t\le 1} |e^{it(-\Delta f|$ 0 < ≤ 1 , when $\{t_{n}\}$ { } contained in Lorentz space $\ell ^{r,\infty}$ ℓ r , ∞ . Consequently, our results provide seemingly optimal higher dimensions, which extend recent work Dimou and Seeger, Li, Wang, Yan dimensions. approach based a localization argument also works for other dispersive equations provides alternative proofs previous sequential convergence.