BOUNDEDNESS OF GENERALIZED HIGHER COMMUTATORS OF MARCINKIEWICZ INTEGRALS

作     者：默会霞 陆善镇 Mo Huixia School of Science,Beijing University of Post and Telecommunications,Beijing 100876,China Lu Shanzhen School of Mathematical Sciences,Beijing Normal University,Beijing 100875,China

作者机构：School of Science Beijing University of Post and TelecommunicationsBeijing 100876China School of Mathematical Sciences Beijing Normal UniversityBeijing 100875China 

出 版 物：《Acta Mathematica Scientia》 (数学物理学报（B辑英文版）)

年 卷 期：2007年第27卷第4期

页      面：852-866页

核心收录：

学科分类：07[理学] 070104[理学-应用数学] 0805[工学-材料科学与工程（可授工学、理学学位）] 0704[理学-天文学] 0701[理学-数学] 

基　　金：Supported by National 973 Project(G.19990751) the SEDF of China(20040027001) 

主　　题：Generalized higher commutator of Marcinkiewicz integral Hardy space Lipschitz space 

摘      要：Let b = （b1,…,bm） be a finite family of locally integrable functions. Then, we introduce generalized higher commutator of Marcinkiwicz integral as follows：（ μΩ^b^→（f）（x）=（∫ 0^∞｜FΩ^b^→,t（f）（x）｜^2t/dt）^1/2,where（FΩ^b^→,t（f）（x）=1/t∫｜x-y｜≤t Ω（x-y）/｜x-y｜^n-1 Лj=1^m（bj（x）-bj（y））f（y）dy.）When（bj∈Aβj,1≤j≤m,0〈βj〈1∑j=1^mβj=β〈n）and Ω is homogeneous of degreezero and satisfies the cancelation condition, we prove that μΩ^b^→is bounded from L^p（R^n）to L^8（R^n）,where1〈p〈βand 1/s=1/p-β/n,Moreover,if Ω also satisties some L^q -Dini condition,then μΩ^b^→ isbounded from L^p（R^n）to Fp^β,∞（R^n）and on certain Hardy *** article extends some known results.