Wavelets, Orlicz spaces, and greedy bases

We study the efficiency of greedy algorithms for N-term wavelet approximation in Orlicz spaces LΦ(Rd). We compute the left and right democracy functions in terms of the fundamental function of LΦ, recovering a recent result of Wojtaszczyk [P. Wojtaszczyk, Greediness of the Haar system in rearrangement invariant spaces, in: T. Figiel, A. Kamont (Eds.), Approximation and Probability, vol. 72, Banach Center Publications, Warszawa, 2006, pp. 385–395], which establishes that wavelet bases can only be greedy when LΦ=Lp for some 1