Gradient estimates for parabolic equations in generalized weighted Morrey spaces

Abstract

We consider the Cauchy-Dirichlet problem for linear divergence form parabolic operators in bounded Reifenberg flat domain. The coefficients supposed to be only measurable in one of the space variables and small BMO with respect to the others. We obtain Caldern-Zygmund type estimate for the gradient of the solution in generalized weighted Morrey spaces with Muckenhoupt weight.