Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: $A_\infty$ condition for general bases revisited: complete
  classification of definitions   We refer to the discussion on different characterizations of the $A_\infty$
class of weights, initiated by Duoandikoetxea, Mart\'in-Reyes, and Ombrosi.
Twelve definitions of the $A_\infty$ condition are considered. For cubes in
$\mathbb{R}^d$ every two conditions are known to be equivalent, while for
general bases we have a trichotomy: equivalence, one-way implication, or no
dependency may occur. In most cases the relations between different conditions
have already been established. Here all the unsolved cases are treated and, as
a result, a full diagram of the said relations is presented.

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The categories of this paper are: hep-lat
35
The categories of this paper are: mtrl-th
18
The categories of this paper are: econ
24
The categories of this paper are: dg-ga
31
The categories of this paper are: ao-sci
8
The categories of this paper are: hep-ex
0
The categories of this paper are: hep-ph
10
The categories of this paper are: q-bio
32
The categories of this paper are: atom-ph
15
The categories of this paper are: nucl-ex
12
The categories of this paper are: nucl-th
37
The categories of this paper are: supr-con
34
The categories of this paper are: chem-ph
27
The categories of this paper are: comp-gas
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The categories of this paper are: astro-ph
36
The categories of this paper are: cmp-lg