Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Hardy Spaces Associated with Ball Quasi-Banach Function Spaces on Spaces
  of Homogeneous Type: Characterizations of Maximal Functions, Decompositions,
  and Dual Spaces   Let $({\mathcal X},\rho,\mu)$ be a space of homogeneous type in the sense of
Coifman and Weiss, and $Y({\mathcal X})$ a ball quasi-Banach function space on
${\mathcal X}$, which supports a Fefferman--Stein vector-valued maximal
inequality, and the boundedness of the powered Hardy--Littlewood maximal
operator on its associate space. The authors first introduce the Hardy space
$H_{Y}^*({\mathcal X})$, associated with $Y({\mathcal X})$, via the grand
maximal function, and then establish its various real-variable
characterizations, respectively, in terms of radial or non-tangential maximal
functions, atoms or finite atoms, and molecules. As an application, the authors
give the dual space of $H_{Y}^*({\mathcal X})$, which proves to be a ball
Campanato-type function space associated with $Y({\mathcal X})$. All these
results have a wide range of generality and, particularly, even when they are
applied to variable Hardy spaces, the obtained results are also new. The major
novelties of this article exist in that, to escape the reverse doubling
condition of $\mu$ and the triangle inequality of $\rho$, the authors cleverly
construct admissible sequences of balls, and fully use the geometrical
properties of ${\mathcal X}$ expressed by dyadic reference points or dyadic
cubes and, to overcome the difficulty caused by the lack of the good dense
subset of $H_{Y}^*({\mathcal X})$, the authors further prove that $Y({\mathcal
X})$ can be embedded into the weighted Lebesgue space with certain special
weight, and then can fully use the known results of the weighted Lebesgue
space.

0
The categories of this paper are: hep-ph
37
The categories of this paper are: supr-con
24
The categories of this paper are: dg-ga
29
The categories of this paper are: funct-an
26
The categories of this paper are: bayes-an
28
The categories of this paper are: alg-geom
19
The categories of this paper are: eess
13
The categories of this paper are: quant-ph
9
The categories of this paper are: nlin
16
The categories of this paper are: stat
25
The categories of this paper are: patt-sol
15
The categories of this paper are: nucl-ex
23
The categories of this paper are: solv-int
32
The categories of this paper are: atom-ph
14
The categories of this paper are: math-ph
35
The categories of this paper are: mtrl-th