Morrey Estimates for Nondivergence Parabolic Operators with Discontinuous Coefficients on Homogeneous Groups

Abstract

In this paper, by establishing the boundedness of singular integral operators with variable kernels and their commutators with BMO functions on Morrey spaces of homogeneous groups, we prove a local a prior estimate in Sobolev-Morrey space for solutions to the nondivergence parabolic equation with discontinuous coefficients.