Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the Boundedness of The Bilinear Hilbert Transform along "non-flat"
  smooth curves. The Banach triangle case ($L^r,\: 1\leq r<\infty$)   We show that the bilinear Hilbert transform $H_{\Gamma}$ along curves
$\Gamma=(t,-\gamma(t))$ with $\gamma\in\mathcal{N}\mathcal{F}^{C}$ is bounded
from $L^{p}(\mathbb{R})\times
L^{q}(\mathbb{R})\,\rightarrow\,L^{r}(\mathbb{R})$ where $p,\,q,\,r$ are
H\"older indices, i.e. $\frac{1}{p}+\frac{1}{q}=\frac{1}{r}$, with
$1<p<\infty$, $1<q\leq\infty$ and $1\leq r<\infty$. Here
$\mathcal{N}\mathcal{F}^{C}$ stands for a wide class of smooth "non-flat"
curves near zero and infinity whose precise definition is given in Section 2.
This continues author's earlier work on this topic, extending the boundedness
range of $H_{\Gamma}$ to any triple of indices
$(\frac{1}{p},\,\frac{1}{q},\,\frac{1}{r'})$ within the Banach triangle. Our
result is optimal up to end-points.

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The categories of this paper are: adap-org
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The categories of this paper are: supr-con
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The categories of this paper are: physics
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The categories of this paper are: funct-an
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The categories of this paper are: atom-ph
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The categories of this paper are: chao-dyn
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The categories of this paper are: plasm-ph
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The categories of this paper are: eess
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The categories of this paper are: ao-sci
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The categories of this paper are: alg-geom
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The categories of this paper are: hep-lat
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The categories of this paper are: bayes-an
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The categories of this paper are: q-fin
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The categories of this paper are: quant-ph
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The categories of this paper are: dg-ga
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The categories of this paper are: q-bio