Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Boundedness of Fourier Integral Operators on $\mathcal{F} L^p$ spaces   We study the action of Fourier Integral Operators (FIOs) of H{\"o}rmander's
type on ${\mathcal{F}} L^p({\mathbb {R}}^d_{comp}$, $1\leq p\leq\infty$. We
see, from the Beurling-Helson theorem, that generally FIOs of order zero fail
to be bounded on these spaces when $p\not=2$, the counterexample being given by
any smooth non-linear change of variable. Here we show that FIOs of order
$m=-d|1/2-1/p|$ are instead bounded. Moreover, this loss of derivatives is
proved to be sharp in every dimension $d\geq1$, even for phases which are
linear in the dual variables. The proofs make use of tools from time-frequency
analysis such as the theory of modulation spaces.

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The categories of this paper are: nucl-ex
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The categories of this paper are: supr-con
11
The categories of this paper are: hep-lat
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The categories of this paper are: math-ph
1
The categories of this paper are: cs
26
The categories of this paper are: bayes-an
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The categories of this paper are: ao-sci
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The categories of this paper are: solv-int
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The categories of this paper are: gr-qc
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The categories of this paper are: q-fin
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The categories of this paper are: chao-dyn
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The categories of this paper are: physics
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The categories of this paper are: eess
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The categories of this paper are: dg-ga
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The categories of this paper are: stat
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The categories of this paper are: alg-geom