Boundeness of Vector-valued Martingales on Weak BMO Spaces

doi:10.16046/j.cnki.issn2096-5680.2021.03.015

Journal of Hebei University of Water Resources and Electric Engineering ›› 2021, Vol. 31 ›› Issue (3): 77-80.DOI: 10.16046/j.cnki.issn2096-5680.2021.03.015

• Basic Science Research • Previous Articles

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

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

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）

Abstract

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

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

CLC Number:

O177

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.

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.

References

[1] Herz C. Bounded mean oscillation and regulated martingales[J].Transactions of the American Mathematical Society, 1974,193(193):199-215.
[2] Fefferman C, Stein E M.Hp spaces of several variables[J]. Acta Math, 1972,129:137-193.
[3] Jiao Y. Carleson measures and vector-valued BMO martingales[J].Probab Theory Relat Fields, 2009,145:421-434.
[4] 张超,陈伟,刘培德.利用分数阶Carleson测度刻画BMO^α鞅空间[J].中国科学:数学,2015,45(4):365-372.
[5] 于林,殷樱.弱Lp空间上的基本鞅不等式[J].应用数学,2009,22(2):270-276.
[6] 刘培德.BMO鞅空间上极大算子与均方算子的有界性[J].数学杂志,1990,10(1):39-46.
[7] 王汝慧,于林.分数次Carleson测度与一致凸空间值BMO^α_q(X)鞅[J].应用泛函分析学报,2016,18(4):346-352.
[8] 王汝慧,于林.向量值弱BMO空间上鞅均方算子的有界性[J].数学的实践与认识,2018,3:241-246.
[9] Yu L. Duality theorem for B-valued martingale Orlicz-Hardy spaces associated with concavefunctions[J].Mathematische Nachrichten, 2016,289(5-6):756-774.
[10] Yu L,Wang R H,Zhao S J.Carleson Measures and The Generalized Campanato Spaces of Vector-valued Martingales [J].Acta Mathematica Scientia(English Series),2018,38(6):1779-1788.
[11] 于林.向量值鞅空间理论[M].北京:北京理工大学出版社,2005.
[12] Long R L, Martingale spaces and inequalities[M]. Beijing: Peking University Press,1993.
[13] Weisz F. Martingale Hardy spaces and their applications in fourieranalysis[M]. New York: Lecture Notes in Mathematics, 1568,Springer-Verlag,1994
[14] Hoffmann-J-rgensenJ, Pisier G. The law of large numbers and the central limit theorem in Banachspaces[J]. The Annals of Probability, 1976,4(4):587-599.
[15] Liu P D. Some new results on martingale inequalities and geometry in Banachspaces[J]. Acta Mathematica Scientia, 1992,12B(1):22-32.
[16] Pisier G. Martingales with values in uniformly convex spaces[J]. Israel Journal of Mathematics, 1975,20(3-4):326-350.
[17] 刘培德.鞅与Banach空间几何学[M].北京:科学出版社,2007.

Boundeness of Vector-valued Martingales on Weak BMO Spaces

向量值BMO_q,(X)空间上鞅算子的有界性

PDF

Knowledge

Abstract

Cite this article

share this article

References

Related Articles 1

Recommended Articles

Metrics

Boundeness of Vector-valued Martingales on Weak BMO Spaces

向量值BMOq,(X)空间上鞅算子的有界性

PDF

Knowledge

Abstract

Cite this article

share this article

References

Related Articles 1

Recommended Articles

Metrics

向量值BMO_q,(X)空间上鞅算子的有界性