论文标题
局部Riesz转换和局部耐寒空间，带有有限的几何形状
Local Riesz transform and local Hardy spaces on Riemannian manifolds with bounded geometry
论文作者
论文摘要
我们证明，如果$τ$是一个很大的正数，则原子Goldberg型空间$ \ Mathfrak {h}^1（n）$和空间$ \ m athfrak {非2级riemannian歧管$ n $，ricci曲率从下方和阳性注射率半径界定。我们还将$ \ mathfrak {h}^1（n）$与slice $ n \ times（0，δ）$的谐波函数的空间相关联，$δ> 0 $ himper。
We prove that if $τ$ is a large positive number, then the atomic Goldberg-type space $\mathfrak{h}^1(N)$ and the space $\mathfrak{h}_{\mathcal R_τ}^1(N)$ of all integrable functions on $N$ whose local Riesz transform $\mathcal R_τ$ is integrable are the same space on any complete noncompact Riemannian manifold $N$ with Ricci curvature bounded from below and positive injectivity radius. We also relate $\mathfrak{h}^1(N)$ to a space of harmonic functions on the slice $N\times (0,δ)$ for $δ>0$ small enough.
