Calderón-Zygmund estimates for parabolic p-Laplacian systems with non-divergence form right-hand sides

We establish local Calderón-Zygmund type estimates for weak solutions to nonlinear parabolic systems with p -growth and VMO coefficients. In particular, we prove that if the right-hand side belongs locally to Lμ s L μ s , where the exponent μ μ depends explicitly on p , N , and a prescribed target exponent $$s>p$$ s > p , then the spatial gradient of the solution enjoys improved integrability Du ∈ Lˢ_loc D u ∈ L loc s . The result provides a sharp transfer of integrability from the data to the gradient, consistent with the natural parabolic scaling, and recovers the optimal exponents in the linear case $$p=2$$ p = 2 . The proof combines intrinsic scaling techniques with a Calderón-Zygmund type iteration scheme.