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Cesàro Means of Weighted Orthogonal Expansions on Regular Domains

Author

Listed:
  • Han Feng

    (Department of Mathematics, City University of Hong Kong, Hong Kong, China
    These authors contributed equally to this work.)

  • Yan Ge

    (Department of Mathematics, City University of Hong Kong, Hong Kong, China
    These authors contributed equally to this work.)

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.

Suggested Citation

  • Han Feng & Yan Ge, 2022. "Cesàro Means of Weighted Orthogonal Expansions on Regular Domains," Mathematics, MDPI, vol. 10(12), pages 1-23, June.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:12:p:2108-:d:841261
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