极大高阶交换子的端点估计

Endpoint Estimates for Higher Order Maximal Commutators

该文主要确立了当b∈BMO时,极大高阶奇异积分算子交换子T_(b,m)~*满足如下不等式|{y∈R^n:T_(b,m)~*f(y) >λ}|≤C||b||_(BMO)~m∫_(Rn)(|f(y)|)/λ(1+log(|f(y)|)/λ)~m dy且T_(b,m)~*在L^p(R^n)(1<P<∞)上有界.

In this paper, the authors establish that higher order maximal commutators of singular integral operator T^＊b,m satisfy the following inequality ｜{y∈R^n：Tb,m^＊f（y）〉λ}｜≤C｜｜b｜｜BMO^m∫R^n｜f（y）｜/λ（1＋log＋｜f（y）/λ）^mdy and are bounded on LP（Rn）, 1 〈 p 〈 ∞, when b is a BMO function.