Abstract
Let T be an anisotropic Calderón-Zygmund operator and with
and
being an anisotropic weighted Lipschitz space. The goal of the paper is to give five boundedness theorems of the commutator
. Precisely,
is bounded from
to
, where
,
,
and
;
is bounded from
to
, when
or
,
,
and
;
is bounded from anisotropic weighted Hardy space
to
, if
or
,
and
;
is bounded from
to weak Lebesgue space
with
,
, which are extensions of isotropic settings and new even for the isotropic weighted and anisotropic unweighted settings.
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Acknowledgments
The authors of the paper would like to express grateful thanks to the anonymous referees for their professional comments and suggestions, which are greatly helpful to improve the quality of the paper.
Disclosure statement
No potential conflict of interest was reported by the authors.