More General Step-Weight Functions ϕ

  • Z. Ditzian
  • V. Totik
Part of the Springer Series in Computational Mathematics book series (SSCM, volume 9)


In Section 1.2 three conditions were imposed on ϕ which were the basis of all the proofs up to now. In this chapter we will relax Conditions I and II and will show that in a way III cannot be relaxed without changing the definition of ω ϕ r (f,t) p . For ϕ(x) ~ xβ(0) where β(0) < 0 and ϕ(x) ~ xβ(∞) where β(∞) > 1 we will provide such a change.


Lebesgue Measure Lower Estimate Absolute Continuity Lebesgue Measure Zero Growth Order 
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Copyright information

© Springer-Verlag New York Inc. 1987

Authors and Affiliations

  • Z. Ditzian
    • 1
  • V. Totik
    • 2
  1. 1.Department of MathematicsUniversity of AlbertaEdmontonCanada
  2. 2.Bolyai InstituteAttila Jozsef UniversitySzegedHungary

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