向量值BMOq,(X)空间上鞅算子的有界性

doi:10.16046/j.cnki.issn2096-5680.2021.03.015

河北水利电力学院学报 ›› 2021, Vol. 31 ›› Issue (3): 77-80.DOI: 10.16046/j.cnki.issn2096-5680.2021.03.015

• 基础科学研究 • 上一篇

向量值BMO_q,(X)空间上鞅算子的有界性

王汝慧

汉江师范学院数学与计算机科学学院,湖北省十堰市茅箭区北京南路18号 442000

收稿日期:2021-03-22 修回日期:2021-03-31 出版日期:2021-09-30 发布日期:2021-11-19
作者简介:王汝慧（1993-），女，湖北恩施人，汉江师范学院数学与计算机科学学院助教，硕士，研究方向：鞅论与泛函分析。E-mail：940701931@qq.com
基金资助:
湖北省教育厅科学研究计划指导性项目“小子样条件下基于信息融合理论的可靠性评估方法及应用”（B2020181）

Boundeness of Vector-valued Martingales on Weak BMO Spaces

WANG Ru-hui

School of Math and Computer Science, Hanjiang Normal University, 442000,Shiyan, Hebei,China

Received:2021-03-22 Revised:2021-03-31 Online:2021-09-30 Published:2021-11-19

摘要/Abstract

摘要： 文中证明了当函数:(0,1]→(0,1]时,X同构于q(2≤q<∞)一致凸Banach空间的充分必要条件是鞅算子是(BMO_q,(X),L_q(R))型的,X同构于p(1<p≤2)一致光滑Banach空间的充分必要条件是鞅算子是(L_p(X),BMO^Sp_p,(X))型的。所得结果给出了Banach空间的q一致凸性及p一致光滑性的新等价刻画形式。

关键词: BMO_q,(X)空间, 一致凸Banach空间, 一致光滑Banach空间

Abstract: Let X be a Banachspace, :(0,1]→(0,1]. It is proved that X is isomorphic to a q-uniformly convex Banach spaceif and only if the q-mean-square operator S^(q)(·) for martingales are of types(BMO_q,(X),L_q (R)); and X is isomorphic to a q-uniformly smooth Banach space if and only if the operator for martingales are of types(L_p (X), BMO^S_p_p,(X)). A new characterization of the q-uniformly convexity and p-uniformly smoothness of Banach space is obtained in the result.

Key words: BMO_q,(X) Spaces, q-uniformly convex Banach spaces, q-uniformly smooth Banach space

中图分类号:

O177

王汝慧. 向量值BMO_q,(X)空间上鞅算子的有界性[J]. 河北水利电力学院学报, 2021, 31(3): 77-80.

WANG Ru-hui. Boundeness of Vector-valued Martingales on Weak BMO Spaces[J]. Journal of Hebei University of Water Resources and Electric Engineering, 2021, 31(3): 77-80.

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向量值BMO_q,(X)空间上鞅算子的有界性

Boundeness of Vector-valued Martingales on Weak BMO Spaces

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