Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A polynomial Carleson operator along the paraboloid   In this work we extend consideration of the polynomial Carleson operator to
the setting of a Radon transform acting along the paraboloid in
$\mathbb{R}^{n+1}$ for $n \geq 2$. Inspired by work of Stein and Wainger on the
original polynomial Carleson operator, we develop a method to treat polynomial
Carleson operators along the paraboloid via van der Corput estimates. A key new
step in the approach of this paper is to approximate a related maximal
oscillatory integral operator along the paraboloid by a smoother operator,
which we accomplish via a Littlewood-Paley decomposition and the use of a
square function. The most technical aspect then arises in the derivation of
bounds for oscillatory integrals involving integration over lower-dimensional
sets. The final theorem applies to polynomial Carleson operators with phase
belonging to a certain restricted class of polynomials with no linear terms and
whose homogeneous quadratic part is not a constant multiple of the defining
function $|y|^2$ of the paraboloid in $\mathbb{R}^{n+1}$.

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The categories of this paper are: hep-lat
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The categories of this paper are: gr-qc
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The categories of this paper are: math-ph
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The categories of this paper are: hep-ph
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The categories of this paper are: bayes-an
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The categories of this paper are: funct-an
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The categories of this paper are: nucl-th
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The categories of this paper are: q-fin
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The categories of this paper are: dg-ga
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The categories of this paper are: alg-geom
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The categories of this paper are: cs
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The categories of this paper are: physics
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The categories of this paper are: astro-ph
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The categories of this paper are: chao-dyn
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The categories of this paper are: econ
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The categories of this paper are: q-bio