2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/117791We study the relations between the quaternion $H$-type group and the boundary of the unit ball on two dimensional quaternionic space. The orthogonal projection of the space of square integrable functions defined on quaternion $H$-type group into its subspace of boundary values of $q$-holomorphic functions is consider. The precise form of Cauchy-Szego kernel and the orthogonal projection operator is obtained. The fundamental solution for the operator $Δ_λ$ is found.18 pagesAnalysis of PDEsComplex VariablesDifferential Geometry35H20, 42B30text