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  • 1 Department of Mathematical and Statistical Sciences, University of Alberta, Edmonton, Alberta, Canada, T6G 2G1
  • | 2 Department of Mathematics, University of Manitoba, Winnipeg, Manitoba, Canada, R3T 2N2
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Abstract

For a Banach space B of functions which satisfies for some m>0
∗
a significant improvement for lower estimates of the moduli of smoothness ωr(f,t)B is achieved. As a result of these estimates, sharp Jackson inequalities which are superior to the classical Jackson type inequality are derived. Our investigation covers Banach spaces of functions on ℝd or for which translations are isometries or on Sd−1 for which rotations are isometries. Results for C0 semigroups of contractions are derived. As applications of the technique used in this paper, many new theorems are deduced. An Lp space with 1<p<∞ satisfies () where s=max  (p,2), and many Orlicz spaces are shown to satisfy () with appropriate s.
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  • SJR Hirsch-Index (2018): 36
  • SJR Quartile Score (2018): Q2 Mathematics (miscellaneous)

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Acta Mathematica Hungarica
Language English
Size B5
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Foundation
1950
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per Year
3
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6
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ISSN 0236-5294 (Print)
ISSN 1588-2632 (Online)

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