Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A note on spectral multipliers on Engel and Cartan groups   The aim of this short note is to give examples of $L^p$-$L^q$ bounded
spectral multipliers for operators involving left-invariant vector fields and
their inverses, in the settings of Engel and Cartan groups. The interest in
such examples lies in the fact that a group does not have to have flat
co-adjoint orbits, and that the considered operator is not related to the usual
sub-Laplacian. The discussed examples show how one can still obtain $L^p$-$L^q$
estimates for similar operators in such settings. As immediate consequences,
one gets the corresponding Sobolev-type inequalities and heat kernel estimates.

22
The categories of this paper are: chao-dyn
33
The categories of this paper are: plasm-ph
28
The categories of this paper are: alg-geom
18
The categories of this paper are: econ
27
The categories of this paper are: comp-gas
20
The categories of this paper are: acc-phys
3
The categories of this paper are: physics
23
The categories of this paper are: solv-int
5
The categories of this paper are: gr-qc
24
The categories of this paper are: dg-ga
7
The categories of this paper are: hep-th
29
The categories of this paper are: funct-an
31
The categories of this paper are: ao-sci
25
The categories of this paper are: patt-sol
6
The categories of this paper are: astro-ph
32
The categories of this paper are: atom-ph