Journal d’Analyse Mathématique

, Volume 79, Issue 1, pp 189–200 | Cite as

A modulus of smoothness on the unit sphere

  • Z. Ditzian


For functions onS d−1 (the unit sphere inR d) and, in particular, forfL p(S d−1), we define new simple moduli of smoothness. We relate different orders of these moduli, and we also relate these moduli to best approximation by spherical harmonics of order smaller thann. Our new moduli lead to sharper results than those now available for the known moduli onL p(S d−1).


Banach Space Unit Sphere Spherical Harmonic Triangle Inequality Orthogonal Matrix 
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Copyright information

© The Magnes Press 1999

Authors and Affiliations

  • Z. Ditzian
    • 1
  1. 1.Department of Mathematical SciencesUniversity of AlbertaEdmontonCanada

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