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Operator Valued Hardy Spaces

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The author gives a systematic study of the Hardy spaces of functions with values in the noncommutative $L^p$-spaces associated with a semifinite von Neumann algebra $\mathcal{M}.$ This is motivated by matrix valued Harmonic Analysis , as well as by the recent development of noncommutative martingale inequalities. In this paper noncommutative Hardy spaces are defined by noncommutative Lusin integral function, and it is proved that they are equivalent to those defined by noncommutative Littlewood-Paley G-functions. The main results of this paper include: The analogue in the author's setting of the classical Fefferman duality theorem between $\mathcal{H}^1$ and $\mathrm{BMO}$. The atomic decomposition of the author's noncommutative $\mathcal{H}^1.$ The equivalence between the norms of the noncommutative Hardy spaces and of the noncommutative $L^p$-spaces $(1

Language: English

Pages: 64

Format: Paperback

Publisher: American Mathematical Society(RI)

Release: July 28, 2007

ISBN: 0821839802

ISBN 13: 9780821839805

Operator Valued Hardy Spaces

0/5 ( ratings)

The author gives a systematic study of the Hardy spaces of functions with values in the noncommutative $L^p$-spaces associated with a semifinite von Neumann algebra $\mathcal{M}.$ This is motivated by matrix valued Harmonic Analysis , as well as by the recent development of noncommutative martingale inequalities. In this paper noncommutative Hardy spaces are defined by noncommutative Lusin integral function, and it is proved that they are equivalent to those defined by noncommutative Littlewood-Paley G-functions. The main results of this paper include: The analogue in the author's setting of the classical Fefferman duality theorem between $\mathcal{H}^1$ and $\mathrm{BMO}$. The atomic decomposition of the author's noncommutative $\mathcal{H}^1.$ The equivalence between the norms of the noncommutative Hardy spaces and of the noncommutative $L^p$-spaces $(1

Language: English

Pages: 64

Format: Paperback

Publisher: American Mathematical Society(RI)

Release: July 28, 2007

ISBN: 0821839802

ISBN 13: 9780821839805

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