Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Hardy spaces related to Schr\"odinger operators with potentials which
  are sums of L^p-functions   We investigate the Hardy space H^1_L associated to the Schr\"odinger operator
L=-\Delta+V on R^n, where V=\sum_{j=1}^d V_j. We assume that each V_j depends
on variables from a linear subspace VV_j of \Rn, dim VV_j \geq 3, and V_j
belongs to L^q(VV_j) for certain q. We prove that there exist two distinct
isomorphisms of H^1_L with the classical Hardy space. As a corollary we deduce
a specific atomic characterization of H_L^1. We also prove that the space H_L^1
is described by means of the Riesz transforms R_{L,i} = \partial_i L^{-1/2}.

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The categories of this paper are: cmp-lg
11
The categories of this paper are: hep-lat
29
The categories of this paper are: funct-an
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The categories of this paper are: alg-geom
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The categories of this paper are: ao-sci
7
The categories of this paper are: hep-th
15
The categories of this paper are: nucl-ex
18
The categories of this paper are: econ
25
The categories of this paper are: patt-sol
6
The categories of this paper are: astro-ph
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The categories of this paper are: chem-ph
13
The categories of this paper are: quant-ph
3
The categories of this paper are: physics
30
The categories of this paper are: q-alg
23
The categories of this paper are: solv-int
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The categories of this paper are: adap-org