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.
| Identifer | oai:union.ndltd.org:tamu.edu/oai:repository.tamu.edu:1969.1/4427 |
| Date | 30 October 2006 |
| Creators | Mei, Tao |
| Contributors | Pisier, Gilles |
| Publisher | Texas A&M University |
| Source Sets | Texas A and M University |
| Language | en_US |
| Detected Language | English |
| Type | Book, Thesis, Electronic Dissertation, text |
| Format | 642062 bytes, electronic, application/pdf, born digital |
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