摘要
本文介绍复Ｂａｎａｃｈ空间几何学近年来的发展状况及其与向量值调和分析、Ｂ值鞅理论的联系．文章包括以下内容：１．几个反例；２．复凸性与复凸模；３．解析Ｒａｄｏｎ－Ｎｉｋｏｄｙｍ性质的分析特征；４．解析Ｒａｄｏｎ－Ｎｉｋｏｄｙｍ性质的几何特征；５．几种ＲＮ性质的比较；６．ＰＬ一致凸性的鞅刻画；７．Ｈ一致凸性的鞅刻画；８．向量值Ｈａｒｄｙ与Ｐａｌｅｙ不等式；９．解析ＵＭＤ空间．
In this paper, recent devolopments of geometry of complex Banach spaces and relationships between them and vector-valued harmonic analysis, martingale theory have been introduced. It carries on in the following nine aspects: 1. Some counterexamples; 2. Complex convexity and moduli of complex convexity; 3. Analytic charactorizations of ARNP; 4. Geometric charactorizations of ARNP; 5. Comparation between several RNP’s; 6. Martingale charactorizations for PL uniform convexity; 7. Martingale characterizations for H uniform convexity; 8. Vector valued Hardy and Paley inequalities; 9. AUMD spaces.
出处
《数学进展》
CSCD
北大核心
1998年第1期1-20,共20页
Advances in Mathematics（China）
基金
国家自然科学基金
关键词
复空间几何学
复巴拿赫空间
几何学
geometry of complex Banach space
analytic Radon-Nikodym property
PL-uniform convexity
H uniform convexity
AUMD property
martingale
vector-valued Hardy and Paley inequality
