Exact values of the best one-sided approximation by Haar polynomials have been obtained in the integral and uniform metrics for some classes of the functions of several variables defined using modulus of continuity ω(f;t) and ωρi (f;δ).
International Journal of Advanced Research in Mathematics (Volume 6)
A. N. Shchitov "Best One-Sided Approximation of Some Classes of Functions of Several Variables by Haar Polynomials", International Journal of Advanced Research in Mathematics, Vol. 6, pp. 42-50, 2016