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Abstract
Let be a space of homogeneous type in the sense of Coifman and Weiss. Let
be a family of sublinear operators that include the well-known Calderón–Zygmund operator. The authors prove that the commutator [b, T] is bounded from a Hardy-type subspace
of
to
, where
denotes the Lebesgue space of all integrable functions,
the atomic Hardy space of Coifman and Weiss with the dual space
, b is a non-constant
-function and
. Indeed, the space
is the largest subspace in
that possesses this property. The approach taken in this article adopts the bilinear decomposition theory for the product of functions in
and
.
AMS Subject Classifications:
Notes
No potential conflict of interest was reported by the authors.
Additional information
Funding
This project is supported by the National Natural Science Foundation of China [grant number 11471042], [grant number 11571039], [grant number 11671185]. Der-Chen Chang is partially supported by an NSF [grant number DMS-1408839]; a McDevitt Endowment Fund at Georgetown University.