Optimality of the range for which equivalence between certain measures of smoothness holds

• Autorzy: Z. Ditzian
• Języki publikacji: EN

Abstrakty

EN

Recently it was proved for 1 < p < ∞ that $ω^{m}(f,t)_{p}$, a modulus of smoothness on the unit sphere, and $K̃ₘ(f,t^{m})_{p}$, a K-functional involving the Laplace-Beltrami operator, are equivalent. It will be shown that the range 1 < p < ∞ is optimal; that is, the equivalence $ω^{m}(f,t)_{p} ≈ K̃ₘ(f,t^{r})_{p}$ does not hold either for p = ∞ or for p = 1.

Kategorie tematyczne

• 42B35: Function spaces arising in harmonic analysis
• 41A63: Multidimensional problems (should also be assigned at least one other classification number in this section)
• 41A17: Inequalities in approximation (Bernstein, Jackson, Nikol\cprime ski{\u\i}-type inequalities)

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2010
• Tom: 198
• Numer: 3
• Strony: 271-277

Daty

wydano

2010

Twórcy

autor

Z. Ditzian

• Department of Mathematical and Statistical Sciences, University of Alberta, Edmonton, AB, Canada T6G 2G1

Identyfikatory

DOI

10.4064/sm198-3-6