Weighted Boundedness of Commutators of Generalized Calderón-Zygmund Operators  

作　　者：Cuilan Wu Yunjie Wang Lisheng Shu 

机构地区：[1]School of Mathematics and Statistics, Jiangsu Normal University [2]Kewen Institute, Jiangsu Normal University [3]College of Mathematics and Computer Science, Anhui Normal University

出　　处：《Analysis in Theory and Applications》2018年第3期209-224,共16页分析理论与应用（英文刊）

摘　　要：[b,T] denotes the commutator of generalized Calderon-Zygmund operators T with Lipschitz function b, where b∈Lip;（R;）,（0 <β≤1） and T is aθ（t）-type Calderón-Zygmund operator. The commutator [b,T] generated by b and T is defined by[b,T]f（x）=b（x）Tf（x）-T（bf）(x)=∫k（x,y）(b（x）-b（y）)f（y）dy.In this paper, the authors discuss the boundedness of the commutator [b, T] on weighted Hardy spaces and weighted Herz type Hardy spaces and prove that [b,T] is bounded from H;（ω;） to L;（ω;）, and from HK;(ω;,ω;) to K;(ω;,ω;). The results extend and generalize the well-known ones in [7].[b,T] denotes the commutator of generalized Calderon-Zygmund operators T with Lipschitz function b, where b∈Lip_β(R^n),(0 <β≤1) and T is aθ(t)-type Calderón-Zygmund operator. The commutator [b,T] generated by b and T is defined by[b,T]f(x)=b(x)Tf(x)-T(bf)(x)=∫k(x,y)(b(x)-b(y))f(y)dy.In this paper, the authors discuss the boundedness of the commutator [b, T] on weighted Hardy spaces and weighted Herz type Hardy spaces and prove that [b,T] is bounded from H^p(ω~p) to L^q(ω~q), and from HK_(q1)^(α,p)(ω_1,ω_2^(q1)) to K_(q2)^(α,p)(ω_1,ω_2^(q2)). The results extend and generalize the well-known ones in [7].

关 键 词：COMMUTATOR Lipschitz function weighted hardy space Herz space 

分 类 号：O177[理学—数学]