Littlewood–Paley Theory for Triangle Buildings

For the natural two-parameter filtration (Formula presented.) on the boundary of a triangle building, we define a maximal function and a square function and show their boundedness on (Formula presented.) for (Formula presented.). At the end, we consider (Formula presented.) boundedness of martingale transforms. If the building is of (Formula presented.), then (Formula presented.) can be identified with p-adic Heisenberg group.