  We prove a priori estimates for a class of transverse fully nonlinear
equations on Sasakian manifolds and give some geometric applications such as
the transversion Calabi-Yau theorem for transverse balanced and (strongly)
Gauduchon metrics. We also explain that similar results hold on compact
oriented, taut, transverse Hermitian foliated manifold of complex co-dimension
$n$, and give some geometric applications such as the transverse Calabi-Yau
theorems for transverse Hermitian and (strongly) Gauduchon metrics.
