Local Calderón-Zygmund estimates for parabolic equations in weighted Lebesgue spaces

We prove local Calderón-Zygmund type estimates for the gradient of weak solutions to degenerate or singular parabolic equations of $ p $-Laplacian type with $ p > \frac{2n}{n+2} $ in weighted Lebesgue spaces $ L^q_w $. We introduce a new condition on the weight $ w $ which depends on the intrinsic geometry concerned with the parabolic $ p $-Laplace problems. Our condition is weaker than the one in ^[13], where similar estimates were obtained. In particular, in the case $ p = 2 $, it is the same as the condition of the usual parabolic $ A_q $ weight.