Global Lorentz estimates for nonlinear parabolic equations on nonsmooth domains

Consider the nonlinear parabolic equation in the form u(t) - diva(D u, x, t) = div (vertical bar F vertical bar(p-2) F) in Omega x (0, T), where T > 0 and Omega is a Reifenberg domain. We suppose that the nonlinearity a(xi, x, t) has a small BMO norm with respect to x and is merely measurable and bounded with respect to the time variable t. In this paper, we prove the global Calderon-Zygmund estimates for the weak solution to this parabolic problem in the setting of Lorentz spaces which includes the estimates in Lebesgue spaces. Our global Calderon-Zygmund estimates extend certain previous results to equations with less regularity assumptions on the nonlinearity a(xi, x, t) and to more general setting of Lorentz spaces.