迭代球面平均算子的有界性  

Boundedness of Iterated Spherical Average

作　　者：邵英君 黄强[1] 卜瑞 SHAO Yingjun;HUANG Qiangl;BU Rui(Department of Mathematics,Zhejiang Normal University,Jinhua,Zhejiang,321004,P.R.China;Department of Mathematics,Qingdao University of Science and Technology,Qingdao,Shandong,266061,P.R.China)

机构地区：[1]浙江师范大学数学系,浙江金华321004 [2]青岛科技大学数学系,山东青岛266061

出　　处：《数学进展》2023年第1期176-186,共11页Advances in Mathematics（China）

基　　金：浙江省教育厅一般科研项目(No.Y201738640);国家自然科学基金资助项目(No.11801518);青岛科技大学科研启动基金。

摘　　要：迭代球面平均算子Δ(A_(1))^(N)是调和分析中的重要算子,在逼近论和概率论中都有非常重要的应用,其中Δ是Laplace算子,A_(1)是单位球面平均算子,(A_(1))^(N)是它的N次迭代算子.本文主要研究了该算子在Besov-Lipschitz空间有界性的充分条件和必要条件,同时证明了它在Triebel-Lizorkin空间的有界性,并用此结论改进了其在L^(p)空间有界性的现有结果.The iterated spherical averageΔ(A_(1))^(N)is an important operator in harmonic analysis,and has very important applications in approximation theory and probability theory,whereΔis the Laplacian,A_(1)is the unit spherical average and(A_(1))^(N)is its iteration.In this paper,we mainly study the sufficient and necessary conditions for the boundedness of this operator in Besov-Lipschitz spaces,and prove the boundedness of the operator in Triebel-Lizorkin spaces.Moreover,We use above conclusions to improve the existing results of the boundedness of this operator in L^(p)spaces.

关 键 词：迭代球面平均算子 Besov-Lipschitz空间 TRIEBEL-LIZORKIN空间 L^(p)空间 

分 类 号：O174.2[理学—数学]