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Acta Mathematica Sinica, English Series

, Volume 35, Issue 2, pp 185–203 | Cite as

Inequalities for the Extended Best Polynomial Approximation Operator in Orlicz Spaces

  • Sonia AcinasEmail author
  • Sergio Favier
  • Felipe Zó
Article
  • 18 Downloads

Abstract

In this paper we pursue the study of the best approximation operator extended from LΦ to Lφ, where φ denotes the derivative of the function Φ. We get pointwise convergence for the coefficients of the extended best approximation polynomials for a wide class of function f, closely related to the Calderón–Zygmund class t m p (x) which had been introduced in 1961. We also obtain weak and strong type inequalities for a maximal operator related to the extended best polynomial approximation and a norm convergence result for the coefficients is derived. In most of these results, we have to consider Matuszewska–Orlicz indices for the function φ.

Keywords

Orlicz spaces extended best polynomial approximation pointwise and norm convergence weak and strong type inequalities Orlicz indices 

MR(2010) Subject Classification

05B05 05B25 20B25 

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Notes

Acknowledgements

The authors would like to thank the referee for such valuable comments and suggestions.

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Copyright information

© Institute of Mathematics, Academy of Mathematics and Systems Science (CAS), Chinese Mathematical Society (CAS) and Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Departamento de Matemática, Facultad de Ciencias y Exactas NaturalesUniversidad Nacional de La PampaSanta Rosa, La PampaArgentina
  2. 2.Instituto de Matemática Aplicada San Luis, IMASLUniversidad Nacional de San Luis and CONICETSan LuisArgentina
  3. 3.Departamento de MatemáticaUniversidad Nacional de San LuisSan LuisArgentina

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