二维Hardy空间维林肯型系统的极大算子  

TWO-DIMENSIONAL MAXIMAL OPERATOR OF VILENKIN-LIKE SYSTEM ON HARDY SPACES

作　　者：张学英[1] 王超越 张传洲[1] 肖俊[1] ZHANG Xue-ying;WANG Chao-yue;ZHANG Chuan-zhou;XIAO Jun(College of Science,Wuhan University of Science and Technology,Wuhan 430065,China)

机构地区：[1]武汉科技大学理学院,湖北武汉430065

出　　处：《数学杂志》2023年第5期398-408,共11页Journal of Mathematics

基　　金：Supported by National Natural Science Foundation of China(11871195)。

摘　　要：本文研究二维Hardy空间维林肯型系统的极大算子的有界性.利用原子分解方法,我们证明二维极大算子T_(α)f:=sup(2-α≤n/m≤2α)|f*Pn,m|是从鞅Hardy空间Hp到Lp有界的,其中0<p<1/2,α≥0.作为应用,我们得到二维极大算子σ*f=sup_(2-α≤n/m≤2α)|σn,mf|/([(n+1)(m+1)])1/p-2的有界性证明.通过构造反例,我们证明二维极大算子■不是从鞅Hardr空间H^(p)到L^(p)有界的,其中0<p<1/2.上述结果推广了沃尔什系统、维林肯系统下的已知结论.In this paper,we research the boundedness of two-dimensional maximal operator of Vilenkin-like system on Hardy spaces.By means of atomic decomposition,the two-dimensional maximal operator T_(α)f:=sup_(2~(-α)≤n/m≤2~α)) |f* P_(n,m)| is bounded from H~p to L~p,where 0 p 1/2and α≥ 0.As an application,we prove the boundedness of two-dimensional operator σ~*f=supsup_(2~(-α)≤n/m≤2~α)) |σ_(n,m)f|/([(n+1)(m+1)])~(1/p-2)).By a counterexample,we also prove that two dimensional maximal operator ■ is not bounded from H^(p) to L^(p),where 0 p 1/2.The results as above generalize the known conclusions in Walsh system or in Vilenkin system.

关 键 词：维林肯型系统 极大算子 Dirichlet核 Fejér核 

分 类 号：O174.2[理学—数学]