Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Boundedness of Calder\'on-Zygmund Operators on Non-homogeneous Metric
  Measure Spaces   Let $({\mathcal X}, d, \mu)$ be a separable metric measure space satisfying
the known upper doubling condition, the geometrical doubling condition and the
non-atomic condition that $\mu(\{x\})=0$ for all $x\in{\mathcal X}$. In this
paper, we show that the boundedness of a Calder\'on-Zygmund operator $T$ on
$L^2(\mu)$ is equivalent to that of $T$ on $L^p(\mu)$ for some $p\in (1,
\infty)$, and that of $T$ from $L^1(\mu)$ to $L^{1,\,\infty}(\mu).$ As an
application, we prove that if $T$ is a Calder\'on-Zygmund operator bounded on
$L^2(\mu)$, then its maximal operator is bounded on $L^p(\mu)$ for all $p\in
(1, \infty)$ and from the space of all complex-valued Borel measures on
${\mathcal X}$ to $L^{1,\,\infty}(\mu)$. All these results generalize the
corresponding results of Nazarov et al. on metric spaces with measures
satisfying the so-called polynomial growth condition.

18
The categories of this paper are: econ
34
The categories of this paper are: chem-ph
28
The categories of this paper are: alg-geom
33
The categories of this paper are: plasm-ph
0
The categories of this paper are: hep-ph
9
The categories of this paper are: nlin
3
The categories of this paper are: physics
7
The categories of this paper are: hep-th
6
The categories of this paper are: astro-ph
37
The categories of this paper are: supr-con
8
The categories of this paper are: hep-ex
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The categories of this paper are: nucl-ex
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The categories of this paper are: chao-dyn
4
The categories of this paper are: cond-mat
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The categories of this paper are: dg-ga
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The categories of this paper are: patt-sol