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 $f\in L_1[0,1{]}^d$.