Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Weighted bounds for variational Fourier series   For 1<p<infty and for weight w in A_p, we show that the r-variation of the
Fourier sums of any function in L^p(w) is finite a.e. for r larger than a
finite constant depending on w and p. The fact that the variation exponent
depends on w is necessary. This strengthens previous work of Hunt-Young and is
a weighted extension of a variational Carleson theorem of
Oberlin-Seeger-Tao-Thiele-Wright. The proof uses weighted adaptation of phase
plane analysis and a weighted extension of a variational inequality of
Lepingle.

11
The categories of this paper are: hep-lat
16
The categories of this paper are: stat
30
The categories of this paper are: q-alg
6
The categories of this paper are: astro-ph
4
The categories of this paper are: cond-mat
12
The categories of this paper are: nucl-th
23
The categories of this paper are: solv-int
17
The categories of this paper are: q-fin
34
The categories of this paper are: chem-ph
21
The categories of this paper are: adap-org
28
The categories of this paper are: alg-geom
1
The categories of this paper are: cs
33
The categories of this paper are: plasm-ph
20
The categories of this paper are: acc-phys
31
The categories of this paper are: ao-sci
26
The categories of this paper are: bayes-an