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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
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
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…