P. Jones' interpolation theorem for noncommutative martingale Hardy spaces II

IF 1 2区数学 Q1 MATHEMATICS

Journal of the London Mathematical Society-Second Series Pub Date : 2024-07-17 DOI:10.1112/jlms.12968

Narcisse Randrianantoanina

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引用次数: 0

Abstract

Let $M$ be a semifinite von Neumann algebra equipped with an increasing filtration ${(M_{n})}_{n ⩾ 1}$ of (semifinite) von Neumann subalgebras of $M$ . For $1 ⩽ p ⩽ \infty$ , let $H_{p}^{c} (M)$ denote the noncommutative column martingale Hardy space constructed from column square functions associated with the filtration ${(M_{n})}_{n ⩾ 1}$ and the index $p$ . We prove the following real interpolation identity: If $0 < θ < 1$ and $1 / p = 1 - θ$ , then

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P.非交换马氏哈代空间的琼斯插值定理 II

让 M $\mathcal {M}$ 是一个半有穷 von Neumann 代数，其上有 M $\mathcal {M}$ 的（半有穷）von Neumann 子代数的递增滤波 ( M n ) n ⩾ 1 $(\mathcal {M}_n)_{n\geqslant 1}$ 。对于 1 ⩽ p ⩽ ∞ $1\leqslant p \leqslant \infty$ 、让 H p c ( M ) $\mathcal {H}_p^c(\mathcal {M})$ 表示由与滤波 ( M n ) n ⩾ 1 $(\mathcal {M}_n)_{n\geqslant 1}$ 和索引 p $p$ 相关的列平方函数构造的非交换列鞅哈代空间。我们证明下面的实插值特性：如果 0 < θ < 1 $0<\theta <1$ 和 1 / p = 1 - θ $1/p=1-\theta$ , 那么

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来源期刊

Journal of the London Mathematical Society-Second Series 数学-数学

CiteScore

1.90

自引率

0.00%

发文量

186

审稿时长

6-12 weeks

期刊介绍： The Journal of the London Mathematical Society has been publishing leading research in a broad range of mathematical subject areas since 1926. The Journal welcomes papers on subjects of general interest that represent a significant advance in mathematical knowledge, as well as submissions that are deemed to stimulate new interest and research activity.