Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the embedding of $A_1$ into $A_\infty$   We give a quantitative embedding of the Muckenhoupt class $A_1$ into
$A_\infty$. In particular, we show how $\epsilon$ depends on $[w]_{A_1}$ in the
inequality which characterizes $A_\infty$ weights: \[
  \frac{w(E)}{w(Q)} \leq \biggl( \frac{|E|}{|Q|} \biggr)^\epsilon, \] where $Q$
is any dyadic cube and $E$ is any subset of $Q$. This embedding yields a sharp
reverse-H\"older inequality as an easy corollary.

27
The categories of this paper are: comp-gas
30
The categories of this paper are: q-alg
33
The categories of this paper are: plasm-ph
12
The categories of this paper are: nucl-th
0
The categories of this paper are: hep-ph
23
The categories of this paper are: solv-int
19
The categories of this paper are: eess
37
The categories of this paper are: supr-con
1
The categories of this paper are: cs
5
The categories of this paper are: gr-qc
16
The categories of this paper are: stat
25
The categories of this paper are: patt-sol
31
The categories of this paper are: ao-sci
32
The categories of this paper are: atom-ph
15
The categories of this paper are: nucl-ex
29
The categories of this paper are: funct-an