Lower bounds for the rate of convergence of greedy algorithms

We obtain a lower bound for the rate of convergence of a pure greedy algorithm in the spaces $\mathcal A_0(\mathcal D)$ and $\mathcal A_1(\mathcal D)$, and this bound turns out to be very close to the best known upper bound. We also obtain a precise lower bound for the rate of convergence of the orthogonal greedy algorithm in the space $\mathcal A_0(\mathcal D)$.