Geodesic
The convergence of the greedy algorithm with respect to the Haar system in the space $L_p(0,1)$
Sbornik. Mathematics, Tome 201 (2010) no. 2, pp. 253-288

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The approximation properties of the $X$-greedy algorithm in the space $L_p(0,1)$ are studied. For $1$ estimates for the rate of convergence of the $X$-greedy algorithm with respect to the Haar system are obtained that are close to optimal. Bibliography: 18 titles.
Keywords: greedy algorithms, $m$-term approximations, the Haar system, rate of convergence. 
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     author = {E. D. Livshits},
     title = {The convergence of the greedy algorithm with respect to the {Haar} system in the space $L_p(0,1)$},
     journal = {Sbornik. Mathematics},
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     publisher = {mathdoc},
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     number = {2},
     year = {2010},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_2010_201_2_a3/}
}
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E. D. Livshits. The convergence of the greedy algorithm with respect to the Haar system in the space $L_p(0,1)$. Sbornik. Mathematics, Tome 201 (2010) no. 2, pp. 253-288. http://geodesic.mathdoc.fr/item/SM_2010_201_2_a3/