On the Convergence of a Weak Greedy Algorithm for the Multivariate Haar   Basis
  We define a family of weak thresholding greedy algorithms for the multivariate Haar basis for $L_1[0,1]^d$ ($d \ge 1$). We prove convergence and uniform boundedness of the weak greedy approximants for all $f \in L_1[0,1]^d$. 
S. J. Dilworth, S. Gogyan, and Denka Kutzarova
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