Ces\`aro means of orthogonal expansions in several variables

Abstract

Ces\`aro $(C,\delta)$ means are studied for orthogonal expansions with respect to the weight function $\prod_{i=1}^{d}|x_i|^{2\k_i}$ on the unit sphere, and for the corresponding weight functions on the unit ball and the Jacobi weight on the simplex. A sharp pointwise estimate is established for the $(C,\d)$ kernel with $\d > -1$ and for the kernel of the projection operator, which allows us to derive the exact order for the norm of the Ces\`aro means and the projection operator on these domains.