Weighted estimates for the Calderón commutator. Issue 1 (23rd February 2020) - Chen, Jiecheng; Hu, Guoen
Abstract: In this paper the authors consider the weighted estimates for the Calderón commutator defined by C_m+1, A(a_1, …, a_m;f)(x)=p. v. _RP_2(A; x, y)olimits_j=1^m(A_j(x)-A_j(y))(x-y)^m+2f(y)dy, with P 2 ( A ; x, y ) = A ( x ) − A ( y ) − A ′( y )( x − y ) and A ′ ∈ BMO(ℝ). Dominating this operator by multi(sub)linear sparse operators, the authors establish the weighted bounds from L^p_1(R, w_1) × … × L^p_m+1(R, w_m+1) to L^p(R, ν _1pt w), with p 1, …, p m +1 ∈ (1, ∞), 1/ p = 1/ p 1 + · · · + 1/ p m +1, and 1pt w=(w_1, …, w_m+1)A_P(R^m+1) . The authors also obtain the weighted weak type endpoint estimates for C_m+1, A .