Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: H{\"o}rmander Functional Calculus for Poisson Estimates   The aim of the article is to show a H{\"o}rmander spectral multiplier theorem
for an operator $A$ whose kernel of the semigroup $\exp(-zA)$ satisfies certain
Poisson estimates for complex times $z.$ Here $\exp(-zA)$ acts on
$L^p(\Omega),\,1 < p < \infty,$ where $\Omega$ is a space of homogeneous type
with the additional condition that the measure of annuli is controlled. In most
of the known H{\"o}rmander type theorems in the literature, Gaussian bounds and
self-adjointness for the semigroup are needed, whereas here the new feature is
that the assumptions are the to some extend weaker Poisson bounds, and $\HI$
calculus in place of self-adjointness. The order of derivation in our
H{\"o}rmander multiplier result is typically $\frac{d}{2},$ $d$ being the
dimension of the space $\Omega.$ Moreover the functional calculus resulting
from our H{\"o}rmander theorem is shown to be $R$-bounded. Finally, the result
is applied to some examples.

21
The categories of this paper are: adap-org
27
The categories of this paper are: comp-gas
6
The categories of this paper are: astro-ph
30
The categories of this paper are: q-alg
29
The categories of this paper are: funct-an
32
The categories of this paper are: atom-ph
11
The categories of this paper are: hep-lat
8
The categories of this paper are: hep-ex
26
The categories of this paper are: bayes-an
4
The categories of this paper are: cond-mat
1
The categories of this paper are: cs
25
The categories of this paper are: patt-sol
12
The categories of this paper are: nucl-th
23
The categories of this paper are: solv-int
3
The categories of this paper are: physics
14
The categories of this paper are: math-ph