Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Weak integral conditions for BMO   We study the question of how much one can weaken the defining condition of
BMO. Specifically, we show that if $Q$ is a cube in $\mathbb{R}^n$ and
$h:[0,\infty)\to[0,\infty)$ is such that
$h(t)\underset{t\to\infty}{\longrightarrow}\infty,$ then
  $$ \sup_{J \text{subcube} Q} \frac1{|J|}\int_J h(|\varphi-\frac1{|J|}
\int_J\varphi |)<\infty \Longrightarrow \varphi\in BMO(Q). $$
  Under some additional assumptions on $h$ we obtain estimates on
$\|\varphi\|_{BMO}$ in terms of the supremum above. We also show that even
though the condition $h(t)\underset{t\to\infty}{\longrightarrow}\infty$ is not
necessary for this implication to hold, it becomes necessary if one considers
the dyadic BMO.

14
The categories of this paper are: math-ph
9
The categories of this paper are: nlin
12
The categories of this paper are: nucl-th
0
The categories of this paper are: hep-ph
13
The categories of this paper are: quant-ph
28
The categories of this paper are: alg-geom
37
The categories of this paper are: supr-con
7
The categories of this paper are: hep-th
1
The categories of this paper are: cs
18
The categories of this paper are: econ
11
The categories of this paper are: hep-lat
32
The categories of this paper are: atom-ph
34
The categories of this paper are: chem-ph
26
The categories of this paper are: bayes-an
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The categories of this paper are: gr-qc
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The categories of this paper are: dg-ga