TRIGONOMETRIC QUASI-GREEDY BASESFOR L~p(T;w)

摘要

We give a complete characterization of 2π-periodic weights w for which the usual trigonometric system forms a quasi-greedy basis for L~p(T; 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.