Cesaro Means of Weighted Orthogonal Expansions on Regular Domains

作者：Feng, Han; Ge, Yan^*

来源：Mathematics, 2022, 10(12): 2108.

DOI：10.3390/math10122108

• spherical h-harmonics
• Cesaro means
• Christoffel functions

In this paper, we investigate Cesaro means for the weighted orthogonal polynomial expansions on spheres with weights being invariant under a general finite reflection group on R-d. Our theorems extend previous results only for specific reflection groups. Precisely, we consider the weight function h(kappa)(x) := Pi(nu is an element of R+)vertical bar < x, nu >vertical bar(kappa nu), x is an element of R-d on the unit sphere; the upper estimates of the Cesaro kernels and Cesaro means are obtained and used to prove the convergence of the Cesaro (C, delta) means in the weighted L-p space for delta above the corresponding index. We also establish similar results for the corresponding estimates on the unit ball and the simplex.

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