Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On Fourier integral operators with H\"older-continuous phase   We study continuity properties in Lebesgue spaces for a class of Fourier
integral operators arising in the study of the Boltzmann equation. The phase
has a H\"older-type singularity at the origin. We prove boundedness in $L^1$
with a precise loss of decay depending on the H\"older exponent, and we show by
counterexamples that a loss occurs even in the case of smooth phases. The
results can be seen as a quantitative version of the Beurling-Helson theorem
for changes of variables with a H\"older singularity at the origin. The
continuity in $L^2$ is studied as well by providing sufficient conditions and
relevant counterexamples. The proofs rely on techniques from Time-frequency
Analysis.

3
The categories of this paper are: physics
24
The categories of this paper are: dg-ga
16
The categories of this paper are: stat
8
The categories of this paper are: hep-ex
9
The categories of this paper are: nlin
21
The categories of this paper are: adap-org
12
The categories of this paper are: nucl-th
27
The categories of this paper are: comp-gas
22
The categories of this paper are: chao-dyn
37
The categories of this paper are: supr-con
7
The categories of this paper are: hep-th
32
The categories of this paper are: atom-ph
34
The categories of this paper are: chem-ph
6
The categories of this paper are: astro-ph
0
The categories of this paper are: hep-ph
10
The categories of this paper are: q-bio