... of ω ∈ W 1,p , l over Ω is denoted by ω W 1,p , l ,wα ω W 1,p , l ,wα diam Ω −1 ω p ,Ω, wα ω p ,Ω, wα , 1.6 where α is a real number We denote the exterior derivative by d : D , l → D , l for ... the Aλ3 λ1 , λ2 , Ω condition for r some r > and < λ1 , λ2 , λ3 < ∞; let w1 , w2 ∈ Aλ3 λ1 , λ2 , Ω , if w1 x > 0, w2 x > a.e r and sup B for any ball B ⊂ Ω |B| B λ w1 dx |B| B w2 λ3 r 1 λ2 / r 1 ... ∈ Ar λ1 , λ2 , Ω for some r > 1, < λ1 , λ2 , λ3 < ∞ with w1 x ≥ ε > for any x ∈ Ω Then, there exists a constant C, independent of u, such that G u λ1 loc Lipk , ,w1 ≤ C du λ2 λ3 /s s ,Ω, w2 ,...