Title:Boundedness of operator-valued commutators involving martingale paraproducts
Speaker:Zhenguo Wei (Harbin Institute of Technology)
Time:Friday, April26, 2024, 10:00-11:00
Location: B201-1, Mingde Building
Abstract：Let $1<p<\infty$. We show the boundedness of operator-valued commutators $[\pi_a,M_b]$ on the noncommutative $L_p(L_\infty(\mathbb{R})\otimes \mathcal{M})$ for any von Neumann algebra $\mathcal{M}$, where $\pi_a$ 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.
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