2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/134862We prove that the norm of a weighted composition operator on the Hardy space H^2 of the disk is controlled by the norm of the weight function in the de Branges-Rovnyak space associated to the symbol of the composition operator. As a corollary we obtain a new proof of the boundedness of composition operators on H^2, and recover the standard upper bound for the norm. Similar arguments apply to weighted Bergman spaces. We also show that the positivity of a generalized de Branges-Rovnyak kernel is sufficient for the boundedness of a given composition operator on the standard functions spaces on the unit ball.9 pages, to appear in Proc. Amer. Math SocFunctional Analysis47B33 (primary), 47B32, 46E22 (secondary)text