索伯列夫空间的广义Littlewood-Paley刻画  

Generalized Littlewood-Paley Characterizations of Sobolev Spaces

作　　者：吴太娟 黄强[1] WU Taijuan;HUANG Qiang(Department of Mathematics,Zhejiang Normal University,Jinhua,Zhejiang,321004,P.R.China)

机构地区：[1]浙江师范大学数学系,金华浙江321004

出　　处：《数学进展》2020年第3期349-359,共11页Advances in Mathematics（China）

基　　金：浙江省自然科学基金(No.LQ18A010005);国家自然科学基金(No.11801518).

摘　　要：本文用含有满足阿尔夫斯正则性的测度μ的广义Littlewood-Paley平方函数刻画了分数次索伯列夫空间Wα,p(Rn),1<p<∞.该结果把最新的广义Littlewood-Paley平方函数中的紧支集函数推广到了一般的测度μ,并且刻画了测度的阿尔夫斯正则性和索伯列夫空间正则性指标α之间的关系,同时也消除了紧支集的条件.In this paper,we characterize the fractional Sobolev spaces Wα,p(Rn),1<p<∞,via the generalized Littlewood-Paley square function containing a measureμwhich satisfies the Ahlfors regularity.This result extends the compact support function in the generalized Littlewood-Paley square function to a general measureμ,and characterizes the relationship between the Ahlfors regularity of the measure and the regularity of Sobolev space.It also eliminates the condition of compact support in previous results.

关 键 词：索伯列夫空间 Littlewood-Paley平方函数 阿尔夫斯正则性 

分 类 号：O174.2[理学—数学]