Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On extension of Calder\'on-Zygmund type singular integrals and their
  commutators   Motivated by the recent works [Huan Yu, Quansen Jiu, and Dongsheng Li, 2021]
and [Yanping Chen and Zihua Guo, 2021], we study the following extension of
Calder\'on-Zygmund type singular integrals $$ T_{\beta}f (x) = p.v.
\int_{\mathbb{R}^n} \frac{\Omega(y)}{|y|^{n-\beta}} f(x-y) \, dy, $$ for $0 <
\beta < n$, and their commutators. We establish estimates of these singular
integrals on Lipschitz spaces, Hardy spaces and Muckenhoupt $A_p$-weighted
$L^p$-spaces. We also establish Lebesgue and Hardy space estimates of their
commutators. Our estimates are uniform in small $\beta$, and therefore one can
pass onto the limits as $\beta \to 0$ to deduce analogous estimates for the
classical Calder\'on-Zygmund type singular integrals and their commutators.

26
The categories of this paper are: bayes-an
11
The categories of this paper are: hep-lat
34
The categories of this paper are: chem-ph
37
The categories of this paper are: supr-con
29
The categories of this paper are: funct-an
33
The categories of this paper are: plasm-ph
6
The categories of this paper are: astro-ph
23
The categories of this paper are: solv-int
12
The categories of this paper are: nucl-th
16
The categories of this paper are: stat
10
The categories of this paper are: q-bio
15
The categories of this paper are: nucl-ex
13
The categories of this paper are: quant-ph
8
The categories of this paper are: hep-ex
7
The categories of this paper are: hep-th
25
The categories of this paper are: patt-sol