Local Riesz transform and local Hardy spaces on Riemannian manifolds with bounded geometry

Abstract

We prove that if $\tau$ is a large positive number, then the atomic Goldberg-type space ${\mathfrak{h}}^1(N)$ and the space ${\mathfrak{h}}_{{\mathcal{R}}_{\tau }}^1(N)$ of all integrable functions on $N$ whose local Riesz transform ${\mathcal{R}}_{\tau }$ 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 $N\times (0,\delta )$ for $\delta >0$ small enough.

51 pages

Cited by in corpus (1)

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