A_1 Weights and d-Homogeneous Measures on Ahlfors d-Regular Space  

作　　者：Yu Xia DAI Sheng You WEN Zhi Xiong WEN 

机构地区：[1]Department of Mathematics,Huazhong University of Science and Technology [2]Department of Mathematics,Hubei University

出　　处：《Acta Mathematica Sinica,English Series》2012年第5期901-908,共8页数学学报（英文版）

基　　金：Supported by National Natural Science Foundation of China (Grant Nos. 10971056 and 10771164)

摘　　要：Let X be an Ahlfors d-regular space and rn a d-regular measure on X. We prove that a measure μ on X is d-homogeneous if and only if μ is mutually absolutely continuous with respect to m and the derivative Dmμ（x） is an A1 weight. Also, we show by an example that every Ahlfors d-regular space carries a measure which is d-homogeneous but not d-regular.Let X be an Ahlfors d-regular space and rn a d-regular measure on X. We prove that a measure μ on X is d-homogeneous if and only if μ is mutually absolutely continuous with respect to m and the derivative Dmμ（x） is an A1 weight. Also, we show by an example that every Ahlfors d-regular space carries a measure which is d-homogeneous but not d-regular.

关 键 词：Ahlfors regular space homogeneous measure Ahlfors regular measure WEIGHT 

分 类 号：O177[理学—数学]