Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On Riesz transforms characterization of H^1 spaces associated with some
  Schr\"odinger operators   Let Lf(x)=-\Delta f(x) + V(x)f(x), V\geq 0, V\in L^1_{loc}(R^d), be a
non-negative self-adjoint Schr\"odinger operator on R^d. We say that an
L^1-function f belongs to the Hardy space H^1_L if the maximal function M_L
f(x)=\sup_{t>0} |e^{-tL} f(x)| belongs to L^1(R^d). We prove that under certain
assumptions on V the space H^1_L is also characterized by the Riesz transforms
R_j=\frac{\partial}{\partial x_j} L^{-1/2}, j=1,...,d, associated with L. As an
example of such a potential V one can take any V\geq 0, V\in L^1_{loc}, in one
dimension.

16
The categories of this paper are: stat
19
The categories of this paper are: eess
21
The categories of this paper are: adap-org
31
The categories of this paper are: ao-sci
23
The categories of this paper are: solv-int
17
The categories of this paper are: q-fin
13
The categories of this paper are: quant-ph
9
The categories of this paper are: nlin
6
The categories of this paper are: astro-ph
25
The categories of this paper are: patt-sol
34
The categories of this paper are: chem-ph
7
The categories of this paper are: hep-th
26
The categories of this paper are: bayes-an
30
The categories of this paper are: q-alg
11
The categories of this paper are: hep-lat
37
The categories of this paper are: supr-con