2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/77342This work presents proofs of the main results of (math.QA/9808015), except those on q-Berezin transform to appear in a subsequent work. The notation and the results of (math.QA/9808037) and (math.QA/9808047) are used.LaTeX 2.09, 17 pages, vaksman@ilt.kharkov.ua, sinelshchikov@ilt.kharkov.uaQuantum AlgebraComplex VariablesFunctional Analysis81R50 (Primary) 81Q99 (Secondary)On Function Theory in Quantum Disc: q-Differential Equations and Fourier Transformtext