Abstract:
We describe all sets of dyadic cubes $\Delta=\{\Delta_k\}$ for which
a subsystem of the multivariate Haar system
$\{h_i\colon\operatorname{supp}({h_i})\in\Delta\}$ is quasi-greedy
in $L_1(0,1)^d$. We prove that the greedy algorithm provides a good rate
of convergence for those subsystems.
Keywords:greedy algorithm, quasi-greedy basis, Haar system in $L^1$, subsystem of the Haar system.
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