Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The Variation of the Fractional Maximal Function of a Radial Function   In this paper we study the regularity of the non-centered fractional maximal
operator $M_{\beta}$. As the main result, we prove that there exists
$C(n,\beta)$ such that if $q=n/(n-\beta)$ and $f$ is a radial function, then
$\|DM_{\beta}f\|_{L^{q}(\mathbb{R}^n)}\leq
C(n,\beta)\|Df\|_{L^{1}(\mathbb{R}^n)}$. The corresponding result was
previously known only if $n=1$ or $\beta=0$. Our proofs are almost free from
one-dimensional arguments. Therefore, we believe that the new approach may be
very useful when trying to extend the result for all $f\in
W^{1,1}(\mathbb{R}^n)$.

20
The categories of this paper are: acc-phys
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The categories of this paper are: adap-org
25
The categories of this paper are: patt-sol
11
The categories of this paper are: hep-lat
15
The categories of this paper are: nucl-ex
35
The categories of this paper are: mtrl-th
26
The categories of this paper are: bayes-an
16
The categories of this paper are: stat
24
The categories of this paper are: dg-ga
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The categories of this paper are: alg-geom
32
The categories of this paper are: atom-ph
5
The categories of this paper are: gr-qc
29
The categories of this paper are: funct-an
33
The categories of this paper are: plasm-ph
8
The categories of this paper are: hep-ex
7
The categories of this paper are: hep-th