Hao Zhang

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20242026

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5 papers · 1 filter

math.FA2026

The Endpoint Fractional Riesz Estimate on the Hamming Cube

Zhendong Xu, Hao Zhang

Let $1 < p < 2$ and $D_{j}$ be the discrete partial derivative on the Hamming cube $Ω_{n} = {- 1, 1}^{n}$ . Let $Δ = \sum_{j = 1}^{n} D_{j}$ be the discrete Laplacian.We prove the endpoint inequalit…

math.FA2026

Hypercontractivity for a family of quantum Ornstein-Uhlenbeck semigroups

Longfa Sun, Zhendong Xu, Hao Zhang

We show that a family of quantum Ornstein-Uhlenbeck semigroups is hypercontractive. We also obtain the optimal order of the optimal time up to a constant for those elements whose G…

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.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…