2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/98312We study the asymptotics near the origin of the Fourier transform in weighted Hardy spaces of analytic functions in the upper half-plane, and of the Laplace transform in weighted spaces of entire functions of zero exponential type. These results are applied to two closely related problems posed by E. Dyn'kin: we find the asymptotics of the depth of zero in non-quasianalytic Denjoy-Carleman classes, and of the exact Levinson-Sjoberg majorant.LATeX, 38 pages, preliminary versionComplex VariablesClassical Analysis and ODEstext