d维p-级数域特征系统的(C,α)均值估计(英文)  

MAXIMAL ESTIMATES FOR THE d-DIMENSIONAL(C,α) MEANS OF THE CHARACTER SYSTEM OF p-SERIES FIELD

作　　者：张传洲[1] 张学英[1] 

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》2010年第1期75-81,共7页Journal of Mathematics

基　　金：Supported by Foundation of Hubei Scientific Committee(B20081102)

摘　　要：本文研究了d维p-级数域特征系统的（C,α）均值的问题.利用原子分解方法证明当1≤k≤d max1/（αk＋1）〈q〈∞时，极大算子σ^αf（α=（α1,…,αd））是强（Hq,Lq）型和弱（L1,L1）型。从而序列（σn^αf）几乎处处收敛和依Hq范数收敛于f。上述结果对共轭算子同样成立。此结果推广F.Weisz的结果。The d-dimensional martingale Hardy space Hq is introduced. By the atomic decomposition, it is proved that the maximal operator of the （C, α） α=（α1,…,αd）） means of the character system of p-series field is bounded from Hq to Lq （max1≤k≤d 1/（αk ＋ 1） 〈 q 〈 ∞） and is of weak type （L1, L1）. As a consequence, we obtain that the （C,α） means of a function f ∈ L1 converge a.e. and in Hq norm to the function in question. The same results are proved for the conjugate （C, α） means, too.

关 键 词：鞅HARDY空间 q-原子 (C α)均值 

分 类 号：O211.6[理学—概率论与数理统计]