Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Fourier multipliers on weighted $L^p$ spaces   The paper provides a complement to the classical results on Fourier
multipliers on $L^p$ spaces. In particular, we prove that if $q\in (1,2)$ and a
function $m:\mathbb{R} \rightarrow \mathbb{C}$ is of bounded $q$-variation
uniformly on the dyadic intervals in $\mathbb{R}$, i.e. $m\in
V_q(\mathcal{D})$, then $m$ is a Fourier multiplier on $L^p(\mathbb{R}, wdx)$
for every $p\geq q$ and every weight $w$ satisfying Muckenhoupt's
$A_{p/q}$-condition. We also obtain a higher dimensional counterpart of this
result as well as of a result by E. Berkson and T.A. Gillespie including the
case of the $V_q(\mathcal{D})$ spaces with $q>2$. New weighted estimates for
modified Littlewood-Paley functions are also provided.

20
The categories of this paper are: acc-phys
31
The categories of this paper are: ao-sci
35
The categories of this paper are: mtrl-th
32
The categories of this paper are: atom-ph
15
The categories of this paper are: nucl-ex
7
The categories of this paper are: hep-th
28
The categories of this paper are: alg-geom
1
The categories of this paper are: cs
24
The categories of this paper are: dg-ga
19
The categories of this paper are: eess
0
The categories of this paper are: hep-ph
14
The categories of this paper are: math-ph
36
The categories of this paper are: cmp-lg
18
The categories of this paper are: econ
4
The categories of this paper are: cond-mat
30
The categories of this paper are: q-alg