Boundedness of iterated spherical average

作     者：Rui BU Qiang HUANG Yingjun SHAO Rui BU;Qiang HUANG;Yingjun SHAO

作者机构：Department of MathematicsQingdao University of Science and TechnologyQingdao 266000China Department of Mathematical SciencesZhejiang Normal UniversityJinhua 321000China 

出 版 物：《Frontiers of Mathematics in China》 (中国高等学校学术文摘·数学（英文）)

年 卷 期：2023年第18卷第2期

页      面：125-137页

核心收录：

学科分类：07[理学] 070104[理学-应用数学] 0701[理学-数学] 

主　　题：Iterated spherical average Besov-Lipschitz space Triebel-Lizorkin space L^(p)space 

摘      要：The iterated spherical average∆(A1)^(N)is an important operator in harmonic analysis,and has very important applications in approximation theory and probability theory,where∆is the Laplacian,A_(1)is the unit spherical average and(A1)^(N)is its iteration.In this paper,we mainly study the sufficient and necessary conditions for the boundedness of this operator in Besov-Lipschitz space,and prove the boundedness of the operator in Triebel-Lizorkin space.Moreover,we use above conclusions to improve the existing results of the boundedness of this operator in L^(p)space.