Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Uniform Oscillatory Integral estimates for Convex Phases via Sublevel
  Set estimates   We examine the relation between oscillatory integral estimates and sublevel
set estimates associated to convex functions. Whilst the former implies the
latter in many cases, the reverse requires additional assumptions. Under finite
(line) type assumptions, Bruna, Nagel & Wainger were able to demonstrate a very
precise control of oscillatory integrals with convex phases via their sublevel
sets. Without the finite type assumption, certain erratic behaviour can force
this precise control to fail (Bak, McMichael, Vance & Wainger). We establish
the same precise control under an alternative qualitative geometric assumption.

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The categories of this paper are: q-fin
3
The categories of this paper are: physics
0
The categories of this paper are: hep-ph
4
The categories of this paper are: cond-mat
30
The categories of this paper are: q-alg
28
The categories of this paper are: alg-geom
29
The categories of this paper are: funct-an
36
The categories of this paper are: cmp-lg
15
The categories of this paper are: nucl-ex
18
The categories of this paper are: econ
33
The categories of this paper are: plasm-ph
1
The categories of this paper are: cs
37
The categories of this paper are: supr-con
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The categories of this paper are: astro-ph
8
The categories of this paper are: hep-ex
10
The categories of this paper are: q-bio