Abstract:

Democracy of a basis is a concept closely related to the problem of N-term approximation with elements of the given basis. We will give a proof of the known result that most wavelet bases are democratic for the Lebesgue spaces L^p, 1 ≤ p≤∞. On the other hand, we will give a simple proof of the recently proved result that these wavelet bases are not democratic in the Lorentz spaces L^{p,q}, 1≤ p, q ≤ ∞, unless p=q.