Recent progress on Schatten classes and Riesz transform commutators
This talk is about recent progress on Schatten classes and non-Euclidean Riesz transform commutators. By developing a new approach to bypass the use of Fourier analysis and the standard dyadic structure of Euclidean space, we show that the Schatten norm of several kinds of non-Euclidean Riesz transform commutators can be characterized in terms of Besov norms of the symbol.
Schatten class membership of noncommutative martingale paraproducts
Martingale paraproducts and commutators are well-known as generalizations of Hankel type operators. In this talk, we are concerned about the Schatten class membership of noncommutative martingale paraproducts and operator-valued commutators. We describe their Schatten class memberships in terms of semicommutative Besov spaces. In addition, we also consider the boundedness of operator-valued commutators.
报告题目: A local smoothing estimate on the non-commutative setting
Local smoothing conjecture is one of the most important problems in Harmonic analysis. In this talk, we will review some developments in the local smoothing conjecture in Euclidean space. Then, we will introduce a local smoothing estimate on quantum Euclidean space based on an operator-valued local smoothing estimate. Moreover, we also prove the operator-valued Bourgain's circular maximal theorem. This is joint work with G.Hong and X.Lai.