Approximation of functions of several variables by spherical Riesz means

For even N ≥ 2 and δ 2N-3 (for N-2 or 4 we assume that δ > (N-1)/2) we find asymptotic approximations for the quantity $$E_R^delta (H_{rm N}^omega ) = mathop {sup}limits_{f in H_{rm N}^omega } parallel f(x) - S_R^omega (x,f)parallel _ in (R to infty ),$$ , where S _R ^δ (x,f) is the spherical Riesz mean of order δ of the Fourier kernel of the functionf(x), and H _N ^ω is the class of periodic functions of N variables whose moduli of continuity do not exceed a given convex modulus of continuity ω(δ). For N 2 and δ > 1/2 the result is known.