Author:
Z. Ditzian Department of Mathematical and Statistical Sciences, University of Alberta, Edmonton, Alberta, Canada, T6G 2G1

Search for other papers by Z. Ditzian in
Current site
Google Scholar
PubMed
Close
Restricted access

Abstract

Relations between ωr(f,t)B and ωr+1(f,t)B of the sharp Marchaud and sharp lower estimate-type are shown to be satisfied for some Banach spaces of functions that are not rearrangement invariant. Corresponding results relating the rate of best approximation with ωr(f,t)B for those spaces are also given.

  • [1] Bennet, C. Sharpley, R. 1988 Interpolation of Operators Acad. Press.

  • [2] Dai, F. Ditzian, Z. 2005 Littlewood–Paley theory and sharp Marchaud inequality Acta Sci. Math. (Szeged) 71 6590.

  • [3] Dai, F. Ditzian, Z. 2008 Jackson inequality for Banach spaces on the sphere Acta Math. Hungar. 118 171195 .

  • [4] Dai, F. Ditzian, Z. Huang, H. 2010 Equivalence of measures of smoothness in Lp(Sd−1) 1<p<∞ Studia Mathematica 196 179205 .

  • [5] Dai, F. Ditzian, Z. Tikhonov, S. 2008 Sharp Jackson inequalities J. Approx. Theory 151 86112 .

  • [6] DeVore, R. Lorentz, G. 1993 Constructive Approximation Springer Verlag.

  • [7] Ditzian, Z. 1988 On the Marchaud-type inequality Proc. Amer. Math. Soc. 103 198202 .

  • [8] Ditzian, Z. 1998 Fractional derivatives and best approximation Acta Math. Hungar. 81 323348 .

  • [9] Ditzian, Z. 1999 A modulus of smoothness on the unit sphere J. d'Analyse Math. 79 189200 .

  • [10] Ditzian, Z. 2003 Generalizations of the Wirtinger–Northcott inequality Bull. London Math. Soc. 35 455460 .

  • [11] Ditzian, Z. Prymak, A. 2007 Sharp Marchaud and converse inequalities in Orlicz spaces Proc. Amer. Math. Soc. 135 11151121 .

  • [12] Ditzian, Z. Prymak, A. 2011 Convexity, moduli of smoothness and a Jackson-type inequality Acta Math. Hungar. 130 254285 .

  • [13] Lindenstrauss, Y. Tzafriri, L. 1979 Banach Spaces, Vol. II Springer-Verlag.

  • [14] Stein, E. Weiss, G. 1971 Fourier Analysis on Euclidean Spaces Princeton Univ. Press.

  • [15] Timan, M. F. 1958 Converse theorems of the constructive theory of functions in the space Lp Math. Sborn. 46 125132.

  • [16] Timan, M. F. 1966 On Jackson's theorems in Lp spaces Ukrain Mat. Zh. 18 134137 . (in Russian).

  • [17] Zygmund, A. 1950 A remark on the integral modulus of continuity Univ. Nac. Tucuman Rev. Ser. A7 259269.

  • Collapse
  • Expand

To see the editorial board, please visit the website of Springer Nature.

Manuscript Submission: HERE

For subscription options, please visit the website of Springer Nature.

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)

Monthly Content Usage

Abstract Views Full Text Views PDF Downloads
Dec 2023 20 3 1
Jan 2024 27 4 0
Feb 2024 9 2 1
Mar 2024 6 1 0
Apr 2024 9 0 0
May 2024 20 0 0
Jun 2024 0 0 0