Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Fourier coefficients of functions in power-weighted $L_2$-spaces and
  conditionality constants of bases in Banach spaces   We prove that, given $2<p<\infty$, the Fourier coefficients of functions in
$L_2(\mathbb{T}, \lvert t \rvert^{1-2/p}\, dt)$ belong to $\ell_p$, and that,
given $1<p<2$, the Fourier series of sequences in $\ell_p$ belong
$L_2(\mathbb{T}, \lvert t \rvert^{2/p-1}\, dt)$. Then, we apply these results
to the study of conditional Schauder bases and conditional almost greedy bases
in Banach spaces. Specifically, we prove that, for every $1<p<\infty$ and every
$0\le \alpha<1$, there is a Schauder basis of $\ell_p$ whose conditionality
constants grow as $(m^\alpha)_{m=1}^\infty$, and there is an almost greedy
basis of $\ell_p$ whose conditionality constants grow as $((\log
m)^\alpha)_{m=2}^\infty$.

29
The categories of this paper are: funct-an
12
The categories of this paper are: nucl-th
18
The categories of this paper are: econ
1
The categories of this paper are: cs
7
The categories of this paper are: hep-th
6
The categories of this paper are: astro-ph
36
The categories of this paper are: cmp-lg
13
The categories of this paper are: quant-ph
30
The categories of this paper are: q-alg
31
The categories of this paper are: ao-sci
22
The categories of this paper are: chao-dyn
35
The categories of this paper are: mtrl-th
0
The categories of this paper are: hep-ph
33
The categories of this paper are: plasm-ph
32
The categories of this paper are: atom-ph
25
The categories of this paper are: patt-sol