2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/119464We give a complete characterization of $2π$-periodic weights $w$ for which the usual trigonometric system forms a quasi-greedy basis for $L^p(\bT;w)$, i.e., bases for which simple thresholding approximants converge in norm. The characterization implies that this can happen only for $p=2$ and whenever the system forms a quasi-greedy basis, the basis must actually be a Riesz basis.8 pagesFunctional Analysis42C15text