Acta Mathematica Hungarica
Volume/Issue:
Volume 130: Issue 3
Convexity, moduli of smoothness and a Jackson-type inequality
Authors:
Z. Ditzian Department of Mathematical and Statistical Sciences, University of Alberta, Edmonton, Alberta, Canada, T6G 2G1

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A. Prymak Department of Mathematics, University of Manitoba, Winnipeg, Manitoba, Canada, R3T 2N2e-mail: prymak@gmail.com

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Pages:
254–285
Online Publication Date:
03 Nov 2010
Publication Date:
01 Feb 2011
Article Category:
Research Article
DOI:
https://doi.org/10.1007/s10474-010-0008-8
Keywords:
modulus of smoothness; Jackson inequality; Orlicz space; 41A63; 41A17; 41A25; 46B20; 47D60
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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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Cover Acta Mathematica Hungarica
Acta Mathematica Hungarica
Print ISSN:
0236-5294
Online ISSN:
1588-2632

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Acta Mathematica Hungarica
Language English
Size B5
Year of
Foundation		 1950
Volumes
per Year		 3
Issues
per Year		 6
Founder Magyar Tudományos Akadémia  
Founder's
Address		 H-1051 Budapest, Hungary, Széchenyi István tér 9.
Publisher Akadémiai Kiadó
Springer Nature Switzerland AG
Publisher's
Address		 H-1117 Budapest, Hungary 1516 Budapest, PO Box 245.
CH-6330 Cham, Switzerland Gewerbestrasse 11.
Responsible
Publisher		 Chief Executive Officer, Akadémiai Kiadó
ISSN 0236-5294 (Print)
ISSN 1588-2632 (Online)

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