Cesàro means of orthogonal expansions in several variables

الأصل · EN

Cesàro (C,δ) means are studied for orthogonal expansions with respect to the weight function ∏ᵢ₌₁ᵈ|xᵢ|²ⁱ 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,) kernel with > -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.