Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A Characterization of the boundedness of the median maximal function on
  weighted L^p spaces   We introduce and study the median maximal function \mathcal{M} f, defined in
the same manner as the classical Hardy-Littlewood maximal function, only
replacing integral averages of f by medians throughout the definition. This
change has a qualitative impact on the mapping properties of the maximal
operator: in contrast with the Hardy-Littlewood operator, which is not bounded
on L^1, we prove that \mathcal{M} is bounded on L^p(w) for all 0 < p < \infty,
if and only if w \in A_{\infty}. The characterization is purely qualitative and
does not give the dependence on [w]_{A_{\infty}}. However, the sharp bound
\|\mathcal{M}\|_{L^1(w) \to L^1(w)} \lesssim [w]_{A_1} is established.

16
The categories of this paper are: stat
17
The categories of this paper are: q-fin
30
The categories of this paper are: q-alg
27
The categories of this paper are: comp-gas
5
The categories of this paper are: gr-qc
26
The categories of this paper are: bayes-an
15
The categories of this paper are: nucl-ex
21
The categories of this paper are: adap-org
0
The categories of this paper are: hep-ph
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The categories of this paper are: plasm-ph
35
The categories of this paper are: mtrl-th
32
The categories of this paper are: atom-ph
11
The categories of this paper are: hep-lat
29
The categories of this paper are: funct-an
36
The categories of this paper are: cmp-lg
28
The categories of this paper are: alg-geom