Some sharp inequalities for conditionally symmetric martingales

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 μ\sb{\rm p} is the largest positive zero of the parabolic cylinder function of parameter p, then(UNFORMATTED TABLE OR EQUATION FOLLOWS)$\eqalign{\rm\Vert f\Vert\sb{p} \leq \nu\sb{p}\Vert S(f)\Vert\sb{p}\quad&\rm if\quad 0 < p \le 2,\cr\rm\Vert f\Vert\sb{p} \leq μ\sb{p}\Vert S(f)\Vert\sb{p}\quad&\rm if\quad p \ge 3,\cr\rm\nu\sb{p}\Vert S(f)\Vert\sb{p} \leq \Vert f\Vert\sb{p}\quad&\rm if\quad p \geq 2,\cr}$(TABLE/EQUATION ENDS)and the above inequalities are sharp.

Name thesis:degree_name

Ph.D.

Level thesis:degree_level

Dissertation

Discipline thesis:degree_discipline

Mathematics

Grantor

University of Illinois at Urbana-Champaign

Year dc:date

2011

Author dc:creator

• Wang, Gang

• Mathematics

Statement dc:rights

• Copyright 1989 Wang, Gang

Language dc:language

eng

Identifier

AAI8924965
(UMI)AAI8924965

OAI identifier oai:identifier

oai:www.ideals.illinois.edu:2142/20716