Abstract:In this paper the absolute convergence of the group Fourier transform for the Heisenberg group is investigated. It is proved that the Fourier transform of functions belonging to certain Besov spaces is absolutely convergent. The function spaces are defined in terms of the heat semigroup of the full Laplacian of the Heisenberg group.
Keywords: Besov spaces, Heisenberg groups, group Fourier transform
AMS Subject Classification: 46E35, 43A80