For the natural two-parameter filtration F λ : λ ∈ P on the boundary of a triangle building, we define a maximal function and a square function and show their boundedness on L p ( Ω 0 ) for p ∈ ( 1 , ∞ ) . At the end, we consider L p ( Ω 0 ) boundedness of martingale transforms. If the building is of GL ( 3 , Q p ) , then Ω 0 can be identified with p-adic Heisenberg group.