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

Z. Ditzian

Z. Ditzian

Studia Mathematica, Tome 196 (2010), p. 271-277 / Harvested from The Polish Digital Mathematics Library

Résumé

Recently it was proved for 1 < p < ∞ that $ω^{m} {(f, t)}_{p}$ , a modulus of smoothness on the unit sphere, and $K ̃ ₘ {(f, t^{m})}_{p}$ , 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 $ω^{m} {(f, t)}_{p} \approx K ̃ ₘ {(f, t^{r})}_{p}$ does not hold either for p = ∞ or for p = 1.

Publié le : 2010-01-01

Zbl 1191.42010

EUDML-ID : urn:eudml:doc:285743

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     title = {Optimality of the range for which equivalence between certain measures of smoothness holds},
     journal = {Studia Mathematica},
     volume = {196},
     year = {2010},
     pages = {271-277},
     zbl = {1191.42010},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm198-3-6}
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Z. Ditzian. Optimality of the range for which equivalence between certain measures of smoothness holds. Studia Mathematica, Tome 196 (2010) pp. 271-277. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm198-3-6/