Operator valued Hardy spaces and related subjects
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Date
2006-10-30
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Texas A&M University
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.
Description
Keywords
Hardy Space, BMO Space, Maximal Function, von Neumann algebra, noncommutative Lp space, interpolation, Lusin integral