Cesàro Means of Weighted Orthogonal Expansions on Regular Domains

Han Feng and Yan Ge
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Han Feng: Department of Mathematics, City University of Hong Kong, Hong Kong, China
Yan Ge: Department of Mathematics, City University of Hong Kong, Hong Kong, China

Mathematics, 2022, vol. 10, issue 12, 1-23

Abstract: In this paper, we investigate Cesàro 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 κ ( x ) : = ∏ ν ∈ R + | x , ν | κ ν , x ∈ R d on the unit sphere; the upper estimates of the Cesàro kernels and Cesàro means are obtained and used to prove the convergence of the Cesàro ( C , δ ) means in the weighted L p space for δ above the corresponding index. We also establish similar results for the corresponding estimates on the unit ball and the simplex.

Keywords: spherical h -harmonics; Cesàro means; Christoffel functions (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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