Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Commutators of Hilbert transforms along monomial curves   The Hilbert transforms associated with monomial curves have a natural
non-isotropic structure. We study the commutator of such Hilbert transforms and
a symbol $b$ and prove the upper bound of this commutator when $b$ is in the
corresponding non-isotropic BMO space by using the Cauchy integral trick. We
also consider the lower bound of this commutator by introducing a new testing
BMO space associated with the given monomial curve, which shows that the
classical non-isotropic BMO space is contained in the testing BMO space. We
also show that the non-zero curvature of such monomial curves are important,
since when considering Hilbert transforms associated with lines, the parallel
version of non-isotropic BMO space and testing BMO space have overlaps but do
not have containment.

26
The categories of this paper are: bayes-an
29
The categories of this paper are: funct-an
22
The categories of this paper are: chao-dyn
17
The categories of this paper are: q-fin
18
The categories of this paper are: econ
9
The categories of this paper are: nlin
31
The categories of this paper are: ao-sci
37
The categories of this paper are: supr-con
4
The categories of this paper are: cond-mat
35
The categories of this paper are: mtrl-th
16
The categories of this paper are: stat
23
The categories of this paper are: solv-int
10
The categories of this paper are: q-bio
12
The categories of this paper are: nucl-th
36
The categories of this paper are: cmp-lg
6
The categories of this paper are: astro-ph