Maximal estimates for fractional Schr\"odinger equations with spatial variable coefficient

Abstract

Let $v(r,t)=\mathcal{T}_tv_0(r)$ be the solution to a fractional Schrodinger equation where the coefficient of Laplacian depends on the spatial variable. We prove some weighted $L^q$ estimates for the maximal operator generated by $\mathcal{T}_t$ with initial data in a Sobolev-type space.

Keywords

• Schrodinger equation with spatial variable coefficient
• maximal estimate
• Hankel-Sobolev space