2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/96170The heat kernel transform H_t for the Heisenberg group is studied in detail. The main result shows that the image of H_t is a direct sum of two weighted Bergman spaces whose associated weighted functions are of oscillatory nature, i.e. attain positive and negative values.26 pages, 1 figure.Extended final version. To appear in JFA. We would like to express our sincere gratitude to a referee who read the manuscript very carefully and pointed out several inaccuracies, gaps and mistakesClassical Analysis and ODEsFunctional Analysis22E30text