  For the natural two parameter filtration $(\mathcal{F}_\lambda : \lambda \in
P)$ on the boundary of a triangle building we define a maximal function and a
square function and show their boundedness on $L^p(\Omega_0)$ for $p \in (1,
\infty)$. At the end we consider $L^p(\Omega_0)$ boundedness of martingale
transforms. If the building is of $\text{GL}(3, \mathbb{Q}_p)$ then $\Omega_0$
can be identified with $p$-adic Heisenberg group.
