Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Level set estimates for the discrete frequency function   We introduce the discrete frequency function as a possible new approach to
understanding the discrete Hardy-Littlewood maximal function. Considering that
the discrete Hardy-Littlewood maximal function is given at each integer by the
supremum of averages over intervals of integer length, we define the discrete
frequency function at that integer as the value at which the supremum is
attained. After verifying that the function is well-defined, we investigate
size and smoothness properties of this function.

7
The categories of this paper are: hep-th
15
The categories of this paper are: nucl-ex
3
The categories of this paper are: physics
37
The categories of this paper are: supr-con
0
The categories of this paper are: hep-ph
4
The categories of this paper are: cond-mat
5
The categories of this paper are: gr-qc
35
The categories of this paper are: mtrl-th
23
The categories of this paper are: solv-int
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The categories of this paper are: q-bio
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The categories of this paper are: eess
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The categories of this paper are: acc-phys
21
The categories of this paper are: adap-org
24
The categories of this paper are: dg-ga
13
The categories of this paper are: quant-ph
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The categories of this paper are: patt-sol