Cesàro means of orthogonal expansions in several variables

Abstract

Cesàro $(C,\delta )$ 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 Cesàro means and the projection operator on these domains.

Cited by in corpus (1)

• Boundedness of projection operators and Cesàro means in weighted $L^p$ space on the unit sphere