Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: $A_p$ weights and Quantitative Estimates in the Schr\"odinger Setting   Suppose $L=-\Delta+V$ is a Schr\"odinger operator on $\mathbb{R}^n$ with a
potential $V$ belonging to certain reverse H\"older class $RH_\sigma$ with
$\sigma\geq n/2$. The aim of this paper is to study the $A_p$ weights
associated to $L$, denoted by $A_p^L$, which is a larger class than the
classical Muckenhoupt $A_p$ weights. We first establish the "exp--log" link
between $A_p^L$ and $BMO_L$ (the BMO space associated with $L$), which is the
first extension of the classical result to a setting beyond the Laplace
operator. Second, we prove the quantitative $A_p^L$ bound for the maximal
function and the maximal heat semigroup associated to $L$. Then we further
provide the quantitative $A_{p,q}^L$ bound for the fractional integral operator
associated to $L$. We point out that all these quantitative bounds are known
before in terms of the classical $A_{p,q}$ constant. However, since
$A_{p,q}\subset A_{p,q}^L$, the $A_{p,q}^L$ constants are smaller than
$A_{p,q}$ constant. Hence, our results here provide a better quantitative
constant for maximal functions and fractional integral operators associated to
$L$.

28
The categories of this paper are: alg-geom
15
The categories of this paper are: nucl-ex
9
The categories of this paper are: nlin
37
The categories of this paper are: supr-con
7
The categories of this paper are: hep-th
19
The categories of this paper are: eess
30
The categories of this paper are: q-alg
5
The categories of this paper are: gr-qc
33
The categories of this paper are: plasm-ph
21
The categories of this paper are: adap-org
13
The categories of this paper are: quant-ph
31
The categories of this paper are: ao-sci
12
The categories of this paper are: nucl-th
0
The categories of this paper are: hep-ph
3
The categories of this paper are: physics
34
The categories of this paper are: chem-ph