Inequalities for martingales taking values in 2-convex Banach spaces

被引：0

作者：

Osekowski, Adam ^{[1
]}

机构：

[1] Univ Warsaw, Dept Math Informat & Mech, PL-02097 Warsaw, Poland

来源：

STATISTICS & PROBABILITY LETTERS | 2014年 / 84卷

关键词：

Martingale; Square function; Banach space; Hilbert space; 2-convex space; DIFFERENCE-SEQUENCES;

D O I：

10.1016/j.spl.2013.09.032

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

We study sharp square function inequalities for martingales taking values in a 2-convex Banach space B. We show that an appropriate weak-type bound holds true if and only if B is isometric to a Hilbert space. (C) 2013 Elsevier By. All rights reserved.

引用

页码：102 / 107

页数：6

共 11 条

[1]

[Anonymous], 1991, T AM MATH SOC

[2] MARTINGALE INEQUALITIES [J].

BOLLOBAS, B .

MATHEMATICAL PROCEEDINGS OF THE CAMBRIDGE PHILOSOPHICAL SOCIETY, 1980, 87 (MAY) :377-382

[3] SOME REMARKS ON BANACH-SPACES IN WHICH MARTINGALE DIFFERENCE-SEQUENCES ARE UNCONDITIONAL [J].

BOURGAIN, J .

ARKIV FOR MATEMATIK, 1983, 21 (02) :163-168

[4]

Burkholder D. L., 1989, ALMOST EVERYWHERE CO, P159

[5]

BURKHOLDER D. L., 1991, LECT NOTES MATH, V1464, P1

[6] A GEOMETRICAL CHARACTERIZATION OF BANACH-SPACES IN WHICH MARTINGALE DIFFERENCE-SEQUENCES ARE UNCONDITIONAL [J].

BURKHOLDER, DL .

ANNALS OF PROBABILITY, 1981, 9 (06) :997-1011

[7]

Figiel T., 1990, London Math. Soc. Lecture Note Ser., V158, P95

[8]

Godefroy G., 2001, HDB GEOMETRY BANACH, VI, P781

[9] ON FOURIER MULTIPLIER TRANSFORMATIONS OF BANACH-VALUED FUNCTIONS [J].

MCCONNELL, TR .

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 1984, 285 (02) :739-757

[10] On the best constant in the weak type inequality for the square function of a conditionally symmetric martingale [J].

Osekowski, Adam .

STATISTICS & PROBABILITY LETTERS, 2009, 79 (13) :1536-1538

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