2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/67890A sequence of points $z_k$ in the unit disk is said to be thin for a given decrease function $ρ$, if there is a nontrivial bounded holomorphic function such that the infinite series $\sum_k ρ(1-|z_k|)|f(z_k)|$ converges. All sequences will be assumed hyperbolically separated. We give necessary and sufficient conditions for the problem of thinness of a sequence to be non-trivial (one way or the other), and for two different decrease functions to give rise to the same thin sequences. Along the way, some concrete conditions (necessary or sufficient) for a sequence to be thin are obtained.15 pages, LaTeX; some typos corrected. To appear in the issue of Complex Variables dedicated to the memory of Matts EssenComplex VariablesClassical Analysis and ODEs30D50text