Operator Valued Hardy Spaces and Related Subjects
Author | : Tao Mei |
Publisher | : |
Total Pages | : |
Release | : 2006 |
ISBN-10 | : OCLC:86076935 |
ISBN-13 | : |
Rating | : 4/5 ( Downloads) |
Download or read book Operator Valued Hardy Spaces and Related Subjects written by Tao Mei and published by . This book was released on 2006 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: 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