Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Operator-valued local Hardy spaces   This paper gives a systematic study of operator-valued local Hardy spaces.
These spaces are localizations of the Hardy spaces defined by Tao Mei, and
share many properties with Mei's Hardy spaces. We prove the ${\rm h}_1$-$\rm
bmo$ duality, as well as the ${\rm h}_p$-${\rm h}_q$ duality for any conjugate
pair $(p,q)$ when $1<p< \infty$. We show that ${\rm h}_1(\mathbb{R}^d, \mathcal
M)$ and ${\rm bmo}(\mathbb{R}^d, \mathcal M)$ are also good endpoints of
$L_p(L_\infty(\mathbb{R}^d) \overline{\otimes} \mathcal M)$ for interpolation.
We obtain the local version of Calder\'on-Zygmund theory, and then deduce that
the Poisson kernel in our definition of the local Hardy norms can be replaced
by any reasonable test function. Finally, we establish the atomic decomposition
of the local Hardy space ${\rm h}_1^c(\mathbb{R}^d,\mathcal M)$.

32
The categories of this paper are: atom-ph
30
The categories of this paper are: q-alg
27
The categories of this paper are: comp-gas
17
The categories of this paper are: q-fin
22
The categories of this paper are: chao-dyn
9
The categories of this paper are: nlin
25
The categories of this paper are: patt-sol
36
The categories of this paper are: cmp-lg
4
The categories of this paper are: cond-mat
20
The categories of this paper are: acc-phys
31
The categories of this paper are: ao-sci
8
The categories of this paper are: hep-ex
14
The categories of this paper are: math-ph
10
The categories of this paper are: q-bio
26
The categories of this paper are: bayes-an
5
The categories of this paper are: gr-qc