Boundedness of operator-valued commutators involving martingale paraproducts
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866913576707424256 |
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| author | Wei, Zhenguo Zhang, Hao |
| author_facet | Wei, Zhenguo Zhang, Hao |
| contents | Let $1<p<\infty$. We show the boundedness of operator-valued commutators $[π_a,M_b]$ on the noncommutative $L_p(L_\infty(\mathbb{R})\otimes \mathcal{M})$ for any von Neumann algebra $\mathcal{M}$, where $π_a$ is the $d$-adic martingale paraproduct with symbol $a\in BMO^d(\mathbb{R})$ and $M_b$ is the noncommutative left multiplication operator with $b\in BMO^d_\mathcal{M}(\mathbb{R})$. Besides, we consider the extrapolation property of semicommutative $d$-adic martingale paraproducts in terms of the $BMO^d_\mathcal{M}(\mathbb{R})$ space. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2401_08729 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Boundedness of operator-valued commutators involving martingale paraproducts Wei, Zhenguo Zhang, Hao Operator Algebras Functional Analysis Let $1<p<\infty$. We show the boundedness of operator-valued commutators $[π_a,M_b]$ on the noncommutative $L_p(L_\infty(\mathbb{R})\otimes \mathcal{M})$ for any von Neumann algebra $\mathcal{M}$, where $π_a$ is the $d$-adic martingale paraproduct with symbol $a\in BMO^d(\mathbb{R})$ and $M_b$ is the noncommutative left multiplication operator with $b\in BMO^d_\mathcal{M}(\mathbb{R})$. Besides, we consider the extrapolation property of semicommutative $d$-adic martingale paraproducts in terms of the $BMO^d_\mathcal{M}(\mathbb{R})$ space. |
| title | Boundedness of operator-valued commutators involving martingale paraproducts |
| topic | Operator Algebras Functional Analysis |
| url | https://arxiv.org/abs/2401.08729 |