Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Carleson's theorem with quadratic phase   Carleson's theorem on the pointwise convergence of Fourier series provides
bounds for a maximal operator, with the maximum taken over all choices of
linear functions of a phase argument. We extend this to all quadratic choices
of phase functions. Specifically, we show that the maximal operator below maps
$L^p$ into itself for $1<p<\infty$. $$ \sup_a \sup_b |\int
e^{i(ay^2+by)}f(x-y)dy/y| $$

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The categories of this paper are: cs
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The categories of this paper are: cond-mat
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The categories of this paper are: patt-sol
36
The categories of this paper are: cmp-lg
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The categories of this paper are: ao-sci
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The categories of this paper are: nucl-ex
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The categories of this paper are: eess
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The categories of this paper are: adap-org
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The categories of this paper are: q-alg
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The categories of this paper are: atom-ph
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The categories of this paper are: hep-th
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The categories of this paper are: plasm-ph
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The categories of this paper are: nlin
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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: hep-lat