## Files in this item

FilesDescriptionFormat

application/pdf

8924965.pdf (2MB)
(no description provided)PDF

## Description

 Title: Some sharp inequalities for conditionally symmetric martingales Author(s): Wang, Gang Department / Program: Mathematics Discipline: Mathematics Degree Granting Institution: University of Illinois at Urbana-Champaign Degree: Ph.D. Genre: Dissertation Subject(s): Mathematics Abstract: Let f be a conditionally symmetric martingale taking values in a Hilbert space $\rm I\!H$ and let S(f) be its square function. If $\nu\sb{\rm p}$ is the smallest positive zero of the confluent hypergeometric function and $\mu\sb{\rm p}$ is the largest positive zero of the parabolic cylinder function of parameter p, then(UNFORMATTED TABLE OR EQUATION FOLLOWS)\eqalign{\rm\Vert f\Vert\sb{p} \leq \nu\sb{p}\Vert S(f)\Vert\sb{p}\quad&\rm if\quad 0 < p \le 2,\cr\rm\Vert f\Vert\sb{p} \leq \mu\sb{p}\Vert S(f)\Vert\sb{p}\quad&\rm if\quad p \ge 3,\cr\rm\nu\sb{p}\Vert S(f)\Vert\sb{p} \leq \Vert f\Vert\sb{p}\quad&\rm if\quad p \geq 2,\cr}(TABLE/EQUATION ENDS)and the above inequalities are sharp. Issue Date: 1989 Type: Text Language: English URI: http://hdl.handle.net/2142/20716 Rights Information: Copyright 1989 Wang, Gang Date Available in IDEALS: 2011-05-07 Identifier in Online Catalog: AAI8924965 OCLC Identifier: (UMI)AAI8924965
﻿