Operator valued Hardy spaces
著者
書誌事項
Operator valued Hardy spaces
（Memoirs of the American Mathematical Society, no. 881）
American Mathematical Society, 2007
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注記
"July 2007, volume 188, number 881 (second of four numbers)"
Bibliography: p. 63-64
内容説明・目次
内容説明
The author gives a systematic study of the Hardy spaces of functions with values in the noncommutative $Lp$-spaces associated with a semifinite von Neumann algebra $\mathcal{M .$ This is motivated by matrix valued Harmonic Analysis (operator weighted norm inequalities, operator Hilbert transform), 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: (i) The analogue in the author's setting of the classical Fefferman duality theorem between $\mathcal{H 1$ and $\mathrm{BMO $. (ii) The atomic decomposition of the author's noncommutative $\mathcal{H 1.$ (iii) The equivalence between the norms of the noncommutative Hardy spaces and of the noncommutative $Lp$-spaces $(1 \infty )$. (iv) The noncommutative Hardy-Littlewood maximal inequality. (v) A description of BMO as an intersection of two dyadic BMO. (vi) The interpolation results on these Hardy spaces.
目次
Introduction Preliminaries The Duality between $\mathcal H^1$ and BMO The maximal inequality The duality between $\mathcal H^p$ and $\textrm {BMO}^q, 1 < p < 2$ Reduction of BMO to dyadic BMO Interpolation Bibliography.
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