两类向量值BMO_(q)^(φ)(X)空间上鞅的q阶均方算子的有界性  

Boundeness of q-Mean-Square Operator on Two BMO_(q)^(φ)(X)Martingale Spaces

作　　者：王汝慧 覃晓琼 WANG Ru-hui;QIN Xiao-qiong(School of Math and Computer Science,China Hanjiang Normal University,Shiyan 442000,China;Hubei Key Laboratory of Applied Mathemati LS(Hubei University),Wuhan 430062,China)

机构地区：[1]汉江师范学院数学与计算机科学学院,湖北十堰442000 [2]应用数学湖北省重点实验室(湖北大学),湖北武汉430062

出　　处：《数学的实践与认识》2023年第11期178-183,共6页Mathematics in Practice and Theory

基　　金：汉江师范学院校级科研项目(XJ20213501);湖北省高等学校优秀中青年科技创新团队项目:超网络的动力学及控制研究(T2022035);应用数学湖北省重点实验室(湖北大学)开放基金资助(HBAM202003)。

摘　　要：证明了鞅的q阶均方算子S^((q))(.)在两类BMO空间BMO_(q)^(φ)(X)和wBMO_(q)^(φ)(X)上有界的充要条件是X同构于q一致凸Banach空间,所得结果给出了Banach空间的q一致凸性新的等价刻画形式,并且将已有文献中的相关结论进行了推广.It is proved that the q-mean-square operator for martingales S^((q))(·)on BMO_(q)^(φ)(X)and ωBMO_(q)^(φ)(X)are bounded if and only if X is isomorphic to a q-uniformly convex Banach space.As well as,a new characterization of the q-uniformly convexity of Banach space is obtained.The results extend the corresponding results from the vector-valued martingale spaces BMO_(q)^(φ)(X)to BMO_(q)^(φ)(X),from ωBMO_(q)^(φ)(X)to wBMO_(q)^(φ)(X).

关 键 词：BMO_(q)^(φ)(X)空间 wBMO_(q)^(φ)(X)空间 q阶均方算子 一致凸BANACH空间 

分 类 号：O177[理学—数学]