  In this note we generate two local median oscillation decompositions of an
arbitrary measurable function and discuss some applications to
Calder\'{o}n-Zygmund singular integral operators $T$. These applications rely
on the inequality $M^{\sharp}_{0,s}(Tf)(x) \leq c\,Mf(x)$, and we complete the
results given here with a discussion of a local version of this estimate.
