Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Weighted $L^p$ Estimates of Kato Square Roots Associated to Degenerate
  Elliptic Operators   Let $w$ be a Muckenhoupt $A_2(\mathbb{R}^n)$ weight and
$L_w:=-w^{-1}\mathop\mathrm{div}(A\nabla)$ the degenerate elliptic operator on
the Euclidean space $\mathbb{R}^n$, $n\geq 2$. In this article, the authors
establish some weighted $L^p$ estimates of Kato square roots associated to the
degenerate elliptic operators $L_w$. More precisely, the authors prove that,
for $w\in A_{p}(\mathbb{R}^n)$, $p\in(\frac{2n}{n+1},\,2]$ and any $f\in
C^\infty_c(\mathbb{R}^n)$, $\|L_w^{1/2}(f)\|_{L^p(w,\,\mathbb{R}^n)}\sim
\|\nabla f\|_{L^p(w,\,\mathbb{R}^n)}$, where $C_c^\infty(\mathbb{R}^n)$ denotes
the set of all infinitely differential functions with compact supports.

10
The categories of this paper are: q-bio
17
The categories of this paper are: q-fin
19
The categories of this paper are: eess
30
The categories of this paper are: q-alg
37
The categories of this paper are: supr-con
20
The categories of this paper are: acc-phys
28
The categories of this paper are: alg-geom
31
The categories of this paper are: ao-sci
25
The categories of this paper are: patt-sol
4
The categories of this paper are: cond-mat
23
The categories of this paper are: solv-int
33
The categories of this paper are: plasm-ph
14
The categories of this paper are: math-ph
29
The categories of this paper are: funct-an
13
The categories of this paper are: quant-ph
8
The categories of this paper are: hep-ex