Hao Zhang

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20242026

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6 papers · 1 filter

math.FA2024

Complex median method and Schatten class membership of commutators

Zhenguo Wei, Hao Zhang

This article is devoted to the study of the Schatten class membership of commutators involving singular integral operators. We utilize martingale paraproducts and Hytönen's dyadic…

math.CV2024

Weighted norm inequalities of various square functions and Volterra integral operators on the unit ball

Changbao Pang, Maofa Wang, Bang Xu +1

In this paper, we investigate various square functions on the complex unit ball. We prove the weighted inequalities of the Lusin area integral associated with Poisson integral in t…

math.FA2024

On the boundedness and Schatten class property of noncommutative martingale paraproducts and operator-valued commutators

Zhenguo Wei, Hao Zhang

We study the Schatten class membership of semicommutative martingale paraproducts and use the transference method to describe Schatten class membership of purely noncommutative mar…

math.FA2024

Best constants in the vector-valued Littlewood-Paley-Stein theory

Guixiang Hong, Zhendong Xu, Hao Zhang

Let $L$ be a sectorial operator of type $α$ ( $0 \leq α < π /2$ ) on $L^{2} (R^{d})$ with the kernels of ${e^{- t L}}_{t > 0}$ satisfying certain size and regularity conditions. Defi…

math.OA2024

On the best constants of the noncommutative Littlewood-Paley-Stein inequalities

Zhenguo Wei, Hao Zhang

Let $1 < p < \infty$ . Let ${T_{t}}_{t > 0}$ be a noncommutative symmetric diffusion semigroup on a semifinite von Neumann algebra $M$ , and let ${P_{t}}_{t > 0}$ be its associated…

math.OA2024

Boundedness of operator-valued commutators involving martingale paraproducts

Zhenguo Wei, Hao Zhang

Let $1 < p < \infty$ . We show the boundedness of operator-valued commutators $[π_{a}, M_{b}]$ on the noncommutative $L_{p} (L_{\infty} (R) \otimes M)$ for any von Neumann algebr…