各向异性分数次积分算子的加权范数不等式（英文）  

WEIGHTED NORM INEQUALITIES FOR ANISOTROPIC FRACTIONAL INTEGRAL OPERATORS

作　　者：孙瑞瑞[1] 李金霞[1] 李宝德[1] SUN Rui-rui;LI Jin-xia;LI Bao-de(College of Mathematics and System Science,Xinjiang University,Urumqi 830035,Chin)

机构地区：[1]新疆大学数学与系统科学学院,新疆乌鲁木齐830046

出　　处：《数学杂志》2018年第4期643-654,共12页Journal of Mathematics

基　　金：Supported by the National Natural Science Foundation of China(11461065;11661075);a Cultivate Project for Young Doctor from Xinjiang Uyghur Autonomous Region(qn2015bs003)

摘　　要：设A是一个扩张矩阵,α∈[0,1),p:=1/α且函数v满足各向异性Muckenhoupt Ap,∞(A)权条件.本文研究了各向异性分数次积分算子的有界性的问题.利用L(p,∞)空间的Holder不等式和范数‖·‖p,1的σ-次可加性得到了各向异性分数次积分算子关于权vp的一些加权范数不等式.这些结果是Muckenhoupt和Wheeden的结果[6]在各向异性情形下的推广.Let A be an expansive dilation, α ∈（0, 1）, p ：= 1/α and function v satisfy the anisotropic Muckenhoupt condition Ap, ∞（A）. In this paper, we study the boundedness of anisotropic fractional integral operators. By L（p, ∞） H¨older＇s inequality and the σ-subaddictive property of ‖·‖ p, 1, we obtain some weighted norm inequalities for anisotropic fractional integral operators associated with the weight vp, which are anisotropic extension of Muckenhoupt and Wheeden [6].

关 键 词：各向异性 Muckenhoupt权 分数次积分算子 BMO空间 

分 类 号：O174.2[理学—数学]