Electronic Journal of Differential Equations, Vol. 2023 (2023), No. 67, pp. 1-14.

Title: Boundedness on generalized Morrey spaces for the Schr\"odinger  operator with 
potential in a reverse Holder class
       
Authors: Guiyun Wang (Zhejiang Inst. of Communications, Hangzhou, China)
         Shenzhou Zheng (Beijing Jiaotong Univ., Beijing, China)
         
Abstract:
In this article, we  prove  boundedness for the Hessian  of 
a Schrodinger  operator with weak regularity on the coefficients, 
and potentials satisfying the reverse Holder condition.
This is done in in generalized Morrey spaces, and in vanishing generalized Morrey spaces.
On the Schrodinger operator $L=-a_{ij}(x)D_{ij}+V(x)$ it is assumed that
$a_{ij}\in \rm{BMO}_{\theta}(\rho)$ (a generalized Morrey space) and that
$V(x)\in B^*_{n/2}$ (a reverse Holder class).

Submitted May 29, 2023. Published October 13, 2023.
Math Subject Classifications: 35J10, 42B35, 42B20.
Key Words: Schrodinger operators; reverse Holder class;  generalized Morrey space; 
 vanishing generalized Morrey space; BMO-theta-rho coefficients.