Global weighted Orlicz estimates for parabolic measure data problems: Application to estimates in variable exponent spaces

We consider a nonlinear parabolic equation with measurable nonlinearity in a nonsmooth bounded domain when the right-hand side is a finite signed Radon measure. Under optimal regularity assumptions on the nonlinearity and the boundary of the domain, we prove a global Calderón-Zygmund type estimate in weighted Orlicz spaces. As an application we obtain such an estimate in variable exponent spaces, which gives an alternative proof for this new result in the literature.