End-point Estimates and Multi-parameter Paraproducts on Higher Dimensional Tori

与凸集相关的双线性乘子的副乘积

Paraproducts for bilinear multipliers associated with convex sets

本文研究与凸集相关的双线性乘子，证明奇异副乘积在局部 $L^2$ 范围内的有界性，并分别在指数边界曲线和高阶空隙条件下给出结果。

Higher order Journe commutators and characterizations of multi-parameter BMO

We consider iterated commutators of multiplication by a symbol function and tensor products of Hilbert or Riesz transforms. We establish mixed BMO classes of symbols that characterize boundedness of these objects in $L^p$. Little BMO and product BMO, big Hankel operators and iterated commutators are the base cases of our results. We use operator theoretical methods and existing profound results on iterated commutators for the Hilbert transform case, while the general result in several variables is obtained through the construction of a Journé operator that models the behavior of the multiple H…

Global Rigidity of Higher Rank Anosov Actions on Tori and Nilmanifolds

We show that sufficiently irreducible Anosov actions of higher rank abelian groups on tori and nilmanifolds are smoothly conjugate to affine actions.