  In this paper, we establish continuous bilinear decompositions that arise in
the study of products between elements in martingale Hardy spaces $ H^p\
(0<p\leqslant 1) $ and functions in their dual spaces. Our decompositions are
based on martingale paraproducts. As a consequence of our work, we also obtain
analogous results for dyadic martingales on spaces of homogeneous type equipped
with a doubling measure.
