Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: $\mathbf A_1$-regularity and boundedness of Calder\'on-Zygmund
  operators. II   A proof is given for the "only if" part of the result stated in the previous
paper of the series that a suitably nondegenerate Calder\'on-Zygmund operator
$T$ is bounded in a Banach lattice $X$ on $\mathbb R^n$ if and only if the
Hardy-Littlewood maximal operator $M$ is bounded in both $X$ and $X'$, under
the assumption that $X$ has the Fatou property and $X$ is $p$-convex and
$q$-concave with some $1 < p, q < \infty$. We also get rid of a fixed point
theorem in the proof of the main lemma and give an improved version of an
earlier result concerning the divisibility of $\mathrm {BMO}$-regularity.

36
The categories of this paper are: cmp-lg
11
The categories of this paper are: hep-lat
28
The categories of this paper are: alg-geom
13
The categories of this paper are: quant-ph
37
The categories of this paper are: supr-con
16
The categories of this paper are: stat
7
The categories of this paper are: hep-th
34
The categories of this paper are: chem-ph
21
The categories of this paper are: adap-org
19
The categories of this paper are: eess
8
The categories of this paper are: hep-ex
17
The categories of this paper are: q-fin
22
The categories of this paper are: chao-dyn
6
The categories of this paper are: astro-ph
33
The categories of this paper are: plasm-ph
30
The categories of this paper are: q-alg