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 II   Let $H:=-\Delta+V$ be a nonnegative Schr\"odinger operator on $L^2({\bf
R}^N)$, where $N\ge 2$ and $V$ is a radially symmetric inverse square
potential. Let $\|\nabla^\alpha e^{-tH}\|_{(L^{p,\sigma}\to L^{q,\theta})}$ be
the operator norm of $\nabla^\alpha e^{-tH}$ from the Lorentz space
$L^{p,\sigma}({\bf R}^N)$ to $L^{q,\theta}({\bf R}^N)$, where
$\alpha\in\{0,1,2,\dots\}$. We establish both of upper and lower decay
estimates of $\|\nabla^\alpha e^{-tH}\|_{(L^{p,\sigma}\to L^{q,\theta})}$ and
study sharp decay estimates of $\|\nabla^\alpha e^{-tH}\|_{(L^{p,\sigma}\to
L^{q,\theta})}$. Furthermore, we characterize the Laplace operator $-\Delta$
from the view point of the decay of $\|\nabla^\alpha
e^{-tH}\|_{(L^{p,\sigma}\to L^{q,\theta})}$.

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The categories of this paper are: adap-org
31
The categories of this paper are: ao-sci
0
The categories of this paper are: hep-ph
1
The categories of this paper are: cs
35
The categories of this paper are: mtrl-th
18
The categories of this paper are: econ
4
The categories of this paper are: cond-mat
23
The categories of this paper are: solv-int
37
The categories of this paper are: supr-con
16
The categories of this paper are: stat
12
The categories of this paper are: nucl-th
14
The categories of this paper are: math-ph
28
The categories of this paper are: alg-geom
10
The categories of this paper are: q-bio
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The categories of this paper are: atom-ph
9
The categories of this paper are: nlin