Abstract
This article is the second part of two works by the same authors on the same topic. Let be a space of homogeneous type in the sense of Coifman and Weiss. In this article, the authors introduce the notion of paraproducts on
and obtain their boundedness from
into
for any given
satisfying
, where
, for any given
, denotes the Hardy space on
. Moreover, the authors also establish the endpoint boundedness of these paraproducts on
when p or q is ∞ or 1 with
or
replaced by
,
or
, and hence give a complete picture on the boundedness of paraproducts on
. The main novelty of this article is the avoidance of dependence on the reverse doubling assumption of the considered measure μ, which is achieved by fully using the geometrical properties of
expressed via its equipped quasi-metric d, dyadic reference points and dyadic cubes.
2010 Mathematics Subject Classifications:
Acknowledgements
The second author would like to express his deep thanks to Ziyi He for a helpful discussion on the proof of Theorem 2.1.
Disclosure statement
No potential conflict of interest was reported by the author(s).