Atomic decomposition of Hardy type spaces on certain noncompact manifolds

Details Atomic decomposition of Hardy type spaces on certain noncompact manifolds Atomic decomposition of Hardy type spaces on certain noncompact manifolds

2010-02-05

arxiv.org/abs/1002.1161v1

Mathematics

Functional Analysis

22 pages

Scientific paper

In this paper we consider a complete connected noncompact Riemannian manifold
M with bounded geometry and spectral gap. We prove that the Hardy type spaces
X^k(M), introduced in a previous paper of the authors, have an atomic
characterization. As an application, we prove that the Riesz transforms of even
order 2k are bounded from X^k(M) to L^1(M)and on L^p(M) for 1

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