Quasi-greedy property of subsystems of the multivariate Haar system

摘要

We describe all sets of dyadic cubes Delta = {Delta(k)} for which a subsystem of the multivariate Haar system {h(i) : supp(h(i)) is an element of Delta} is quasi-greedy in L-1(0, 1)(d). We prove that the greedy algorithm provides a good rate of convergence for those subsystems.