Nonlinear Haar Approximation of Functions with Bounded Mixed Derivative

Abstract The paper is devoted to the nonlinear approximation by Haar wavelets of periodic and non-periodic functions with bounded mixed derivative. We obtain exact in order sense estimates for the degree of best m-term and Greedy Haar approximation of such classes in two variables. We introduce the non-periodic classes of functions with bounded mixed derivative of order less than 1 to do that.