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

We prove local Calderon-Zygmund type estimates for the gradient of weak solutions to degenerate or singular parabolic equations of p-Laplacian type with p > 2n/n+2 in weighted Lebesgue spaces L-w(q). 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.