Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Weak type bounds for rough maximal singular integrals near $L^1$   In this paper it is shown that for $\Omega\in L\log L(\mathbb{S}^{d-1})$, the
rough maximal singular integral operator $T_\Omega^*$ is of weak type
$L\log\log L(\mathbb{R}^d)$. Furthermore, for $w\in A_1$ and $\Omega\in
L^\infty(\mathbb{S}^{d-1})$, it is shown that $T_\Omega^*$ is of weak type
$L\log\log L(w)$ with weight dependence
$[w]_{A_1}[w]_{A_{\infty}}\log([w]_{A_{\infty}}+1),$ which is same as the best
known constant for the singular integral $T_\Omega$.

18
The categories of this paper are: econ
4
The categories of this paper are: cond-mat
20
The categories of this paper are: acc-phys
14
The categories of this paper are: math-ph
5
The categories of this paper are: gr-qc
12
The categories of this paper are: nucl-th
25
The categories of this paper are: patt-sol
32
The categories of this paper are: atom-ph
16
The categories of this paper are: stat
27
The categories of this paper are: comp-gas
28
The categories of this paper are: alg-geom
17
The categories of this paper are: q-fin
30
The categories of this paper are: q-alg
1
The categories of this paper are: cs
35
The categories of this paper are: mtrl-th
6
The categories of this paper are: astro-ph