| 任颜波.弱Orlicz鞅空间的弱原子分解及其应用[J].数学年刊A辑,2015,36(2):119~128 |
| 弱Orlicz鞅空间的弱原子分解及其应用 |
| Weak Atomic Decompositions of Weak OrliczMartingale Spaces and Applications |
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| DOI： |
| 中文关键词: 鞅,弱Orlicz空间,
原子分解, 有界次线性算子, Marcinkiewicz型插值定理 |
| 英文关键词:Martingale, Weak Orlicz spaces, Atomic decomposition, Bounded
sublinear operator, Marcinkiewicz-type interpolation theorem |
| 基金项目:本文受到国家自然科学基金 (No.11301152), 河南省教育厅科学技术研究重点项目
(No.13B110999)和河南科技大学博士科研启动基金(No.09001772)的资助. |
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| 中文摘要: |
| 对3类由凹函数生成的弱Orlicz鞅空间建立了相应的弱原子分解.
作为应用, 首先给出了这些弱Orlicz鞅空间上次线性算子有界的一个充分条件,
并在此基础上证明了一些弱型鞅不等式,
然后证明了关于这些弱Orlicz鞅空间的Marcinkiewicz 型插值定理. |
| 英文摘要: |
| In this paper, weak atomic decompositions of three kinds of weak Orlicz martingale
spaces generated by concave functions are established. As applications, the author
first gives a sufficient condition for a sublinear operator to be bounded on weak Orlicz martingale
spaces, and based on this, some weak-type martingale inequalities are proved. Then,
the author proves a Marcinkiewicz-type interpolation theorem for weak Orlicz martingale
spaces. |
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