Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Maximal function, Littlewood--Paley theory, Riesz transform and atomic
  decomposition in the multi-parameter flag setting   In this paper, we develop via real variable methods various characterisations
of the Hardy spaces in the multi-parameter flag setting. These
characterisations include those via, the non-tangential and radial maximal
function, the Littlewood--Paley square function and area integral, Riesz
transforms and the atomic decomposition in the multi-parameter flag setting.
The novel ingredients in this paper include (1) establishing appropriate
discrete Calder\'on reproducing formulae in the flag setting and a version of
the Plancherel--P\'olya inequalities for flag quadratic forms; (2) introducing
the maximal function and area function via flag Poisson kernels and flag
version of harmonic functions; (3) developing an atomic decomposition via the
finite speed propagation and area function in terms of flag heat semigroups. As
a consequence of these real variable methods, we obtain the full
characterisations of the multi-parameter Hardy space with the flag structure.

4
The categories of this paper are: cond-mat
25
The categories of this paper are: patt-sol
22
The categories of this paper are: chao-dyn
33
The categories of this paper are: plasm-ph
15
The categories of this paper are: nucl-ex
3
The categories of this paper are: physics
11
The categories of this paper are: hep-lat
17
The categories of this paper are: q-fin
31
The categories of this paper are: ao-sci
24
The categories of this paper are: dg-ga
37
The categories of this paper are: supr-con
27
The categories of this paper are: comp-gas
9
The categories of this paper are: nlin
26
The categories of this paper are: bayes-an
16
The categories of this paper are: stat
13
The categories of this paper are: quant-ph