Lipschitz estimates for commutators of singular integral operators associated with the sections

摘要

Let H be Monge-Ampère singular integral operator, b∈LipFβ, and 1/q = 1/p − β. It is proved that the commutator [b, H] is bounded from L^p(ℝⁿ, dμ) to L^q(ℝⁿ, dμ) for 1  p  1/β and from HFp(Rn) to L^q(ℝⁿ, dμ) for 1/(1 + β)  p ≤ 1. For the extreme case p = 1/(1 + β), a weak estimate is given.