Operator valued Hardy spaces and related subjects
Abstract
We give a systematic study of the Hardy spaces of functions with values in
the non-commutative Lp-spaces associated with a semifinite von Neumann algebra
M. This is motivated by matrix valued harmonic analysis (operator weighted norm
inequalities, operator Hilbert transform), as well as by the recent development of
non-commutative martingale inequalities. Our non-commutative Hardy spaces are
defined by non-commutative Lusin integral functions. It is proved in this dissertation
that they are equivalent to those defined by the non-commutative Littlewood-Paley
G-functions.
We also study the Lp boundedness of operator valued dyadic paraproducts and
prove that their Lq boundedness implies their Lp boundedness for all 1 < q < p < âÂÂ.
Subject
Hardy SpaceBMO Space
Maximal Function
von Neumann algebra
noncommutative Lp space
interpolation
Lusin integral
Citation
Mei, Tao (2006). Operator valued Hardy spaces and related subjects. Doctoral dissertation, Texas A&M University. Texas A&M University. Available electronically from https : / /hdl .handle .net /1969 .1 /4427.