A note on limiting Calderon-Zygmund theory for transformed n-Laplace systems in divergence form

We consider rotated n-Laplace systems on the unit ball B₁ ⊂ Rⁿ of the form {align*} -div( Q|∇ u|ⁿ⁻² ∇ u) = div(G), {align*} where u∈ W1,n(B₁;RN), Q∈ W1,n(B₁;SO(N)) and G∈ L( n/n-1,q )(B₁;Rⁿ⊗ RN) for some 0<q<n/n-1. We prove that ∇ u∈ L(n,q(n-1))loc with estimates. As a corollary, we obtain that solutions to Δₙ u ∈ H¹, where H¹ is the Hardy space, have a higher integrability, namely ∇ u ∈ L(n,n-1)loc.