Summability of Product Jacobi Expansions Original Research Article

Orthogonal expansions in product Jacobi polynomials with respect to the weight function Wα, β(x)=∏dj=1 (1−xj)αj (1+xj)βj on [−1, 1]d are studied. For αj, βj>−1 and αj+βj⩾−1, the Cesàro (C, δ) means of the product Jacobi expansion converge in the norm of Lp(Wα, β, [−1, 1]d), 1⩽p<∞, and C([−1, 1]d) if δ>∑j=1d max{αj, βj}+d2+max0, −∑j=1d min{αj, βj}−d+22 .Moreover, for αj, βj⩾−1/2, the (C, δ) means define a positive linear operator if and only if δ⩾∑di=1 (αi+βi)+3d−1.