Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Sharp Bounds for Oscillatory Integral Operators with Homogeneous
  Polynomial Phases   We obtain sharp $L^p$ bounds for oscillatory integral operators with generic
homogeneous polynomial phases in several variables. The phases considered in
this paper satisfy the rank one condition which is an important notion
introduced by Greenleaf, Pramanik and Tang. Under certain additional
assumptions, we can establish sharp damping estimates with critical exponents
to prove endpoint $L^p$ estimates.

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The categories of this paper are: acc-phys
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The categories of this paper are: q-fin
1
The categories of this paper are: cs
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The categories of this paper are: bayes-an
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The categories of this paper are: stat
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The categories of this paper are: astro-ph
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The categories of this paper are: alg-geom
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The categories of this paper are: funct-an
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The categories of this paper are: quant-ph
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The categories of this paper are: supr-con
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The categories of this paper are: ao-sci
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The categories of this paper are: hep-ex
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The categories of this paper are: econ
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The categories of this paper are: nlin
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The categories of this paper are: plasm-ph
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The categories of this paper are: adap-org