Optimality of the greedy algorithm for some function classes

The convergence rate of the pure greedy algorithm (PGA) is considered. Upper bounds for the convergence rate of the PGA are obtained in the case of the target function in the classes $\widehat{\mathscr A_\gamma}(\mathscr D)$, $\gamma\geqslant0$, which are extensions of the class $\widehat{\mathscr A_1}(\mathscr D)$. This bound is shown to be sharp in order for $\gamma\geqslant2$.
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