Jackson-type inequality on the sphere

@article{Ditzian2004JacksontypeIO,
  title={Jackson-type inequality on the sphere},
  author={Zeev Ditzian},
  journal={Acta Mathematica Hungarica},
  year={2004},
  volume={102},
  pages={1-36}
}
In a recent paper, I introduced new moduli of smoothness for functions on the sphere which did not use averages and, as a result, had some interesting properties. The direct, Jackson-type, estimate of the best approximation by spherical harmonics using the new moduli will be proved here. Equivalence with the appropriate K-functionals will be given. Relations with the moduli used earlier will be shown and used to prove new results for these moduli.