Electron. J. Differential Equations, Vol. 2018 (2018), No. 139, pp. 1-13.

Maximal estimates for fractional Schrodinger equations with spatial variable coefficient

Bo-Wen Zheng

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.

Submitted May 28, 2017. Published July 3, 2018.
Math Subject Classifications: 35B65, 35Q40, 35Q55.
Key Words: Schrodinger equation with spatial variable coefficient; maximal estimate; Hankel-Sobolev space.

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Bo-wen Zheng
College of Sciences
China Jiliang University
Hangzhou 310018, China
email: bwen_zj1516@126.com, 17a0802126@cjlu.edu.cn

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