Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Three observations on commutators of Singular Integral Operators with
  BMO functions   This paper contains three observations on commutators of Singular Integral
Operators with BMO functions:
  1) The subgaussian local decay for the commutator, namely
\[\frac{1}{|Q|}\left|\left\{x\in Q\, : \,
|[b,T](f\chi_Q)(x)|>M^2f(x)t\right\}\right|\leq c e^{-\sqrt{ct\|b\|_{BMO}}} \]
is sharp, that is, it is subgaussian and not better.
  2) It is not possible to obtain a pointwise control of the commutator by a
finite sum of sparse operators defined with $L\log L$ averages.
  3) If $w\in A_p\setminus A_1$ then $\left\|
wM\left(\frac{f}{w}\right)\right\|_{L^1(\mathbb{R}^n)\rightarrow
L^{1,\infty}(\mathbb{R}^n)}=\infty$.

30
The categories of this paper are: q-alg
23
The categories of this paper are: solv-int
7
The categories of this paper are: hep-th
12
The categories of this paper are: nucl-th
6
The categories of this paper are: astro-ph
27
The categories of this paper are: comp-gas
0
The categories of this paper are: hep-ph
14
The categories of this paper are: math-ph
35
The categories of this paper are: mtrl-th
33
The categories of this paper are: plasm-ph
36
The categories of this paper are: cmp-lg
29
The categories of this paper are: funct-an
28
The categories of this paper are: alg-geom
20
The categories of this paper are: acc-phys
11
The categories of this paper are: hep-lat
19
The categories of this paper are: eess