Cesàro Means of Orthogonal Expansions in Several Variables

Abstract

Cesaro (C,δ) means are studied for orthogonal expansions with respect to the weight function \(\prod_{i=1}^{d}|x_{i}|^{2\kappa_{i}}\) 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,δ) kernel with δ>−1 and for the kernel of the projection operator, which allows us to derive the exact order for the norm of the Cesaro means and the projection operator on these domains.