Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Atomic decomposition of Hardy type spaces on certain noncompact
  manifolds   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<p<\infty.

33
The categories of this paper are: plasm-ph
22
The categories of this paper are: chao-dyn
14
The categories of this paper are: math-ph
30
The categories of this paper are: q-alg
34
The categories of this paper are: chem-ph
28
The categories of this paper are: alg-geom
21
The categories of this paper are: adap-org
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The categories of this paper are: atom-ph
6
The categories of this paper are: astro-ph
13
The categories of this paper are: quant-ph
1
The categories of this paper are: cs
18
The categories of this paper are: econ
27
The categories of this paper are: comp-gas
4
The categories of this paper are: cond-mat
7
The categories of this paper are: hep-th
24
The categories of this paper are: dg-ga