2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/66514We define an analog of the Poisson integral formula for a family of the non-commutative Lobachevsky spaces. The $q$-Fourier transform of the Poisson kernel is expressed through the $q$-Bessel-Macdonald function.LateX, 15 pages, Contribution in the Fridrich Karpelevich memorial volumeQuantum Algebra17Bxx, 42Cxxtext