Strong Differential Subordination and Sharp Inequalities for Orthogonal Processes

被引：0

作者：

Adam Osękowski

机构：

[1] University of Warsaw,Department of Mathematics, Informatics and Mechanics

来源：

Journal of Theoretical Probability | 2009年 / 22卷

关键词：

Martingale; Submartingale; Orthogonal processes; Differential subordination; Strong differential subordination; 60G44; 60G48;

D O I：

暂无

中图分类号：

学科分类号：

摘要：

We introduce a strong differential α-subordination for continuous-time processes, which generalizes this notion from the discrete-time setting, due to Burkholder and Choi. Then we determine the best constants in the Lp estimates for a nonnegative submartingale and its strong α-subordinate under an additional assumption on the orthogonality of these two processes.

引用

页码：837 / 855

页数：18

共 12 条

[1]

Bañuelos R.(1995)Sharp inequalities for martingales with applications to the Beurling–Ahlfors and Riesz transformations Duke Math. J. 80 575-600

[2]

Wang G.(1996)Orthogonal martingales under differential subordination and application to Riesz transforms Ill. J. Math. 40 678-691

[3]

Bañuelos R.(1977)Exit times of Brownian motion, harmonic majorization and Hardy spaces Adv. Math. 26 182-205

[4]

Wang G.(1984)Boundary value problems and sharp inequalities for martingale transforms Ann. Probab. 12 647-702

[5]

Burkholder D.L.(1994)Strong differential subordination and stochastic integration Ann. Probab. 22 995-1025

[6]

Burkholder D.L.(1996)A submartingale inequality Proc. Am. Math. Soc. 124 2549-2553

[7]

Burkholder D.L.(1996)The Beurling–Ahlfors transform in ℝ J. Reine Angew. Math. 473 25-57

[8]

Choi C.(2005) and related singular integrals Trans. Am. Math. Soc. 357 1545-1564

[9]

Iwaniec T.(1995)A sharp weak type ( Ann. Probab. 23 522-551

[10]

Martin G.(undefined), undefined undefined undefined-undefined

← 1 2 →