论文标题
部分可观测时空混沌系统的无模型预测
The dual of the Hardy space associated with the Dunkl operators
论文作者
论文摘要
理性的dunkl操作员正在向欧几里得空间上的差分反射操作员通勤与根系相关的$ r^d $，其中包含一些非本地反射术语，并且相关的硬质空间是通过Riesz相对于Dunkl Operators的方式来定义的。本文的目的是证明其双重可以通过$ r^d $上的一类函数来实现，该功能由文本中的$bmc_κ$表示，该功能由特定类型的加权Carleson测量的基本功能组成。我们的方法是“纯粹的分析”，不依赖于原子分解。作为推论，我们在$bmc_κ$中获得了功能的Fefferman-Stein分解。
The rational Dunkl operators are commuting differential-reflection operators on the Euclidean space $R^d$ associated with a root system, that contain some non-local refection terms, and the associated Hardy space is defined by means of the Riesz transforms with respect to the Dunkl operators. The aim of the paper is to prove that its dual can be realized by a class of functions on $R^d$, denoted by $BMC_κ$ in the text, that consists of the underlying functions of a certain type of weighted Carleson measures. Our method is "purely analytic" and does not depend on the atomic decomposition. As a corollary we obtain the Fefferman-Stein decomposition of functions in $BMC_κ$.
