Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: $L^p-L^q$ boundedness of Fourier multipliers associated with the
  anharmonic Oscillator   In this paper we study the $L^p$-$L^q$ boundedness of the Fourier multipliers
in the setting where the underlying Fourier analysis is introduced with respect
to the eigenfunctions of an anharmonic oscillator $A$. Using the notion of a
global symbol that arises from this analysis, we extend a version of the
Hausdorff-Young-Paley inequality that guarantees the $L^p$-$L^q$ boundedness of
these operators for the range $1<p \leq 2 \leq q <\infty$. The boundedness
results for spectral multipliers acquired, yield as particular cases Sobolev
embedding theorems and time asymptotics for the $L^p$-$L^q$ norms of the heat
kernel associated with the anharmonic oscillator. Additionally, we consider
functions $f(A)$ of the anharmonic oscillator on modulation spaces and prove
that Linsk\u ii's trace formula holds true even when $f(A)$ is simply a nuclear
operator.

9
The categories of this paper are: nlin
18
The categories of this paper are: econ
22
The categories of this paper are: chao-dyn
24
The categories of this paper are: dg-ga
15
The categories of this paper are: nucl-ex
19
The categories of this paper are: eess
33
The categories of this paper are: plasm-ph
21
The categories of this paper are: adap-org
17
The categories of this paper are: q-fin
0
The categories of this paper are: hep-ph
36
The categories of this paper are: cmp-lg
35
The categories of this paper are: mtrl-th
16
The categories of this paper are: stat
7
The categories of this paper are: hep-th
34
The categories of this paper are: chem-ph
37
The categories of this paper are: supr-con