Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: $L^p$ bound for the Hilbert transform along variable non-flat curves   We prove the $L^p$ bound for the Hilbert transform along variable non-flat
curves $(t,u(x)[t]^\alpha+v(x)[t]^\beta)$, where $\alpha$ and $\beta$ satisfy
  $\alpha\neq \beta,\ \alpha\neq 1,\ \beta\neq 1.$
  Comparing with the associated theorem in \cite{GHLJ} investigating the case
$\alpha=\beta\neq 1$, our result is more general while the proof is more
involved. To achieve our goal, we divide the frequency of the objective
function into three cases and take different strategies to control these cases.
Furthermore, we need to introduce a "short" shift maximal function
$\mathfrak{M}^{[n]}$ to establish some pointwise estimate.

19
The categories of this paper are: eess
21
The categories of this paper are: adap-org
13
The categories of this paper are: quant-ph
0
The categories of this paper are: hep-ph
32
The categories of this paper are: atom-ph
28
The categories of this paper are: alg-geom
1
The categories of this paper are: cs
15
The categories of this paper are: nucl-ex
7
The categories of this paper are: hep-th
31
The categories of this paper are: ao-sci
26
The categories of this paper are: bayes-an
11
The categories of this paper are: hep-lat
35
The categories of this paper are: mtrl-th
6
The categories of this paper are: astro-ph
30
The categories of this paper are: q-alg
24
The categories of this paper are: dg-ga