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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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