Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Decay estimates for Schr\"odinger heat semigroup with inverse square
  potential in Lorentz spaces   Let $H:=-\Delta+V$ be a nonnegative Schr\"odinger operator on $L^2({\bf
R}^N)$, where $N\ge 2$ and $V$ is an inverse square potential. In this paper we
obtain sharp decay estimates of the operator norms of $e^{-tH}$ and $\nabla
e^{-tH}$ in Lorentz spaces.

1
The categories of this paper are: cs
16
The categories of this paper are: stat
4
The categories of this paper are: cond-mat
6
The categories of this paper are: astro-ph
0
The categories of this paper are: hep-ph
17
The categories of this paper are: q-fin
3
The categories of this paper are: physics
26
The categories of this paper are: bayes-an
33
The categories of this paper are: plasm-ph
8
The categories of this paper are: hep-ex
22
The categories of this paper are: chao-dyn
14
The categories of this paper are: math-ph
9
The categories of this paper are: nlin
24
The categories of this paper are: dg-ga
10
The categories of this paper are: q-bio
18
The categories of this paper are: econ