Consider the nonlinear parabolic equation in the form
$$begin{aligned} u_t-mathrm{div}{mathbf {a}}(D u,x,t)=mathrm{div},(|F|^{p-2}F) quad text {in} quad Omega times (0,T), end{aligned}$$
where
(T>0) and
(Omega ) is a Reifenberg domain. We suppose that the nonlinearity
({mathbf {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 Calderón-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 Calderón-Zygmund estimates extend certain previous results to equations with less regularity assumptions on the nonlinearity
({mathbf {a}}(xi ,x,t)) and to more general setting of Lorentz spaces.
