J. Aust. Math. Soc.
76 (2004), 207221

Boundedness of vectorvalued martingale transforms on extreme points and applications

Teresa Martínez
Departamento de Matemáticas
Universidad Autónoma de Madrid
Ciudad Universitaria de Canto Blanco
28049 Madrid
Spain
teresa.martinez@uam.es



José L. Torrea
Departamento de Matemáticas
Universidad Autónoma de Madrid
Ciudad Universitaria de Canto Blanco
28049 Madrid
Spain
joseluis.torrea@uam.es



Abstract

Let , be a pair of Banach spaces and
be a vector valued martingale transform (with
respect to general filtration) which
maps valued martingales into
valued martingales. Then, the following
statements are equivalent:
is bounded
from into for some
(or equivalently for every
) in the range
;
is bounded from
into
;
is bounded from
into
;
is bounded from
into
. Applications to
and martingale cotype properties are given. We
also prove that the Hardy space
defined in the case of a general filtration has
nice dense sets and nice atomic decompositions if
and only if
has the RadonNikodým property.

Download the article in PDF format (size 141 Kb)


