Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: BMO spaces associated to operators with generalised Poisson bounds on
  non-doubling manifolds with ends   Consider a non-doubling manifold with ends $M = \mathfrak{R}^{n}\sharp\,
{\mathbb R}^{m}$ where $\mathfrak{R}^n=\mathbb{R}^n\times \mathbb{S}^{m-n}$ for
$m> n \ge 3$. We say that an operator $L$ has a generalised Poisson kernel if
$\sqrt{ L}$ generates a semigroup $e^{-t\sqrt{L}}$ whose kernel $p_t(x,y)$ has
an upper bound similar to the kernel of $e^{-t\sqrt{\Delta}}$ where $\Delta$ is
the Laplace-Beltrami operator on $M$. An example for operators with generalised
Gaussian bounds is the Schr\"odinger operator $L = \Delta + V$ where $V$ is an
arbitrary non-negative locally integrable potential. In this paper, our aim is
to introduce the BMO space ${\rm BMO}_L(M)$ associated to operators with
generalised Poisson bounds which serves as an appropriate setting for certain
singular integrals with rough kernels to be bounded from $L^{\infty}(M)$ into
this new ${\rm BMO}_L(M)$. On our ${\rm BMO}_L(M)$ spaces, we show that the
John--Nirenberg inequality holds and we show an interpolation theorem for a
holomorphic family of operators which interpolates between $L^q(M)$ and ${\rm
BMO}_L(M)$. As an application, we show that the holomorphic functional calculus
$m(\sqrt{L})$ is bounded from $L^{\infty}(M)$ into ${\rm BMO}_L(M)$, and
bounded on $L^p(M)$ for $1 < p < \infty$.

30
The categories of this paper are: q-alg
19
The categories of this paper are: eess
34
The categories of this paper are: chem-ph
11
The categories of this paper are: hep-lat
33
The categories of this paper are: plasm-ph
13
The categories of this paper are: quant-ph
7
The categories of this paper are: hep-th
10
The categories of this paper are: q-bio
18
The categories of this paper are: econ
5
The categories of this paper are: gr-qc
32
The categories of this paper are: atom-ph
31
The categories of this paper are: ao-sci
4
The categories of this paper are: cond-mat
26
The categories of this paper are: bayes-an
20
The categories of this paper are: acc-phys
17
The categories of this paper are: q-fin