Boundedness on generalized Morrey spaces for the Schrodinger operator with potential in a reverse Holder class

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 H\"older 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).
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