Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Weighted vector-valued estimates for a non-standard Calder\'on-Zygmund
  operator   In this paper, the author considers the weighted vector-valued estimate for
the operator defined by $$T_Af(x)={\rm
p.\,v.}\int_{\mathbb{R}^n}\frac{\Omega(x-y)}{|x-y|^{n+1}}\big(A(x)-A(y)-\nabla
A(y)\big)f(y){\rm d}y,$$ and the corresponding maximal operator $T_A^*$, where
$\Omega$ is homogeneous of degree zero, has vanishing moment of order one, $A$
is a function in $\mathbb{R}^n$ such that $\nabla A\in {\rm
BMO}(\mathbb{R}^n)$. By a pointwise estimate for $\|\{T_Af_k(x)\}\|_{l^q}$ and
the weighted $L^p$ estimates for the sparse operator
$$\mathcal{A}_{\mathcal{S},\,L(\log
L)^\beta}f(x)=\sum_{Q\in\mathcal{S}}\|f\|_{L(\log L)^{\beta},\,Q}\chi_{Q}(x)
,$$ the author establishes some weak and endpoint quantitative weighted
vector-valued estimates for $T_A$ and $T_A^*$.

32
The categories of this paper are: atom-ph
15
The categories of this paper are: nucl-ex
6
The categories of this paper are: astro-ph
8
The categories of this paper are: hep-ex
10
The categories of this paper are: q-bio
16
The categories of this paper are: stat
19
The categories of this paper are: eess
28
The categories of this paper are: alg-geom
22
The categories of this paper are: chao-dyn
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The categories of this paper are: supr-con
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The categories of this paper are: patt-sol
3
The categories of this paper are: physics
12
The categories of this paper are: nucl-th
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The categories of this paper are: comp-gas
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The categories of this paper are: bayes-an
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The categories of this paper are: econ