Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Riesz transforms associated with higher-order Schr\"odinger type
  operators   In this paper, let $L=L_{0}+V$ be a Schr\"{o}dinger type operator where
$L_{0}$ is higher order elliptic operator with complex coefficients in
divergence form and $V$ is signed measurable function, under the strongly
subcritical assumption on $V$, the authors study the $L^{q}$ boundedness of
Riesz transforms $\nabla^{m}L^{-1/2}$ for $q\leq 2$ and obtain a sharp result.
Furthermore, the authors impose extra regularity assumptions on $V$ to obtain
the $L^{q}$ boundedness of Riesz transforms $\nabla^{m}L^{-1/2}$ for $q>2$. As
an application, the main results can be applied to the operator
$L=(-\Delta)^{m}-\gamma|x|^{-2m}$ for suitable $\gamma$

22
The categories of this paper are: chao-dyn
0
The categories of this paper are: hep-ph
13
The categories of this paper are: quant-ph
24
The categories of this paper are: dg-ga
11
The categories of this paper are: hep-lat
7
The categories of this paper are: hep-th
14
The categories of this paper are: math-ph
1
The categories of this paper are: cs
15
The categories of this paper are: nucl-ex
36
The categories of this paper are: cmp-lg
29
The categories of this paper are: funct-an
30
The categories of this paper are: q-alg
10
The categories of this paper are: q-bio
28
The categories of this paper are: alg-geom
27
The categories of this paper are: comp-gas
21
The categories of this paper are: adap-org