An Upbound of Hausdorff's Dimension of the Divergence Set of the fractional Schrödinger Operator on $H^s(\mathbb R^n)

Dan Li, Junfeng Li, Jie Xiao

This paper shows $$ \sup_{f\in H^s(\mathbb{R}^n)}\dim _H\left\{x\in\mathbb{R}^n:\ \lim_{t\rightarrow0}e^{it(-Δ)^α}f(x)\neq f(x)\right\}\leq n+1-\frac{2(n+1)s}{n}\ \ \text{under}\ \…