Weighted estimates for commutators of anisotropic Calderón-Zygmund operators

Let T be an anisotropic Calderón-Zygmund operator and b∈Lipα,w(Rn,A) with 0<α<1 and Lipα,w(Rn,A) being an anisotropic weighted Lipschitz space. The goal of the paper is to give five boundedness theorems of the commutator [b,T]. Precisely, [b,T] is bounded from Lwq(Rn) to Lw1−qrqr(Rn), where w∈Aqr(A), 1/qr=1/q−α/n, 1<q<n/α and 1<r<∞; [b,T] is bounded from Lwq(Rn) to Lw1−rr(Rn), when w∈A1(A) or w∈Ar(A), 1/r=1/q−α/n, 1<q<n/α and 1<q<r<∞; [b,T] is bounded from anisotropic weighted Hardy space Hwp(Rn,A) to Lw1−rr(Rn), if w∈A1(A) or w∈Ar(A), 1/r=1/p−α/n and n/(n+α)<p≤ 1<r<∞; [b,T] is bounded from Hwn/(n+α)(Rn,A) to weak Lebesgue space L1,∞(Rn) with w∈A1(A), p=n/(n+α), which are extensions of isotropic settings and new even for the isotropic weighted and anisotropic unweighted settings.