Estimation of the best approximation of periodic functions of two variables by an “angle” in the metric of L_p - Konopovich, T. O. (Ukrains’kyi Matematychnyi Zhurnal, 2004)
We obtain upper bounds in terms of Fourier coefficients for the best approximation by an “angle” and for norms in the metric of L_p for functions of two variables defined by trigonometric series with coefficients such that a_l_1 l_2 → 0 as l_1 + l_2 → ∞ and _k_1 = 0^∞ _k_2 = 0^∞ ( _l_1 = k_1 ^∞ _l_2 = k_2 ^∞ | Δ ^12 a_l_1 l_2 | )^p (k_1 + 1)^p - 2 (k_2 + 1)^p - 2 < ∞ for a certain p, 1 < p < ∞.