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Some sharp inequalities for conditionally symmetric martingales

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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
 

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