Abstract: | It is shown that if P m α,β (x) (α, β > ?1, m = 0, 1, 2, …) are the classical Jaboci polynomials, then the system of polynomials of two variables {Ψ mn α,β (x, y)} m,n=0 r = {P m α,β (x)P n α,β (y)} m, n=0 r (r = m + n ≤ N ? 1) is an orthogonal system on the set Ω N×N = ?ub;(x i , y i ) i,j=0 N , where x i and y i are the zeros of the Jacobi polynomial P n α,β (x). Given an arbitrary continuous function f(x, y) on the square ?1, 1]2, we construct the discrete partial Fourier-Jacobi sums of the rectangular type S m, n, N α,β (f; x, y) by the orthogonal system introduced above. We prove that the order of the Lebesgue constants ∥S m, n, N α,β ∥ of the discrete sums S m, n, N α,β (f; x, y) for ?1/2 < α, β < 1/2, m + n ≤ N ? 1 is O((mn) q + 1/2), where q = max?ub;α,β?ub;. As a consequence of this result, several approximate properties of the discrete sums S m, n, N α,β (f; x, y) are considered. |