论文标题
$ l^2 $ riesz在海森伯格小组上的界限的必要条件
Necessary condition for the $L^2$ boundedness of the Riesz transform on Heisenberg groups
论文作者
论文摘要
令$μ$为$ n $ -th Heisenberg Group $ \ mathbb {h}^n $的ra。在本说明中，我们证明，如果$（2n+1）$ - 尺寸（Heisenberg）Riesz在$ \ mathbb {h}^n $上转换为$ l^2（μ）$ - 以及$μ（f）= 0 $，所有Borel套件的所有Borel套件都带有$ \ dim_h（f）\ dim_h（f）\ dim_h（f）\ leq 2 $ $ $ $ $ $ $ $（$ 1）这是1991年盖伊·戴维（Guy David）的结果的海森伯格（Heisenberg）。
Let $μ$ be a Radon measure on the $n$-th Heisenberg group $\mathbb{H}^n$. In this note we prove that if the $(2n+1)$-dimensional (Heisenberg) Riesz transform on $\mathbb{H}^n$ is $L^2(μ)$-bounded, and if $μ(F)=0$ for all Borel sets with $\dim_H(F)\leq 2$, then $μ$ must have $(2n+1)$-polynomial growth. This is the Heisenberg counterpart of a result of Guy David from 1991.
