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Boletín de la Sociedad Matemática Mexicana

, Volume 25, Issue 3, pp 659–672 | Cite as

Nikol’skii inequalities for Lorentz–Zygmund spaces

  • Leo R. Ya. DoktorskiEmail author
  • Dmitrij Gendler
Original Article
  • 86 Downloads

Abstract

Analogs of the Nikol’skii inequality in Lorentz–Zygmund spaces are obtained for functions of the form \(\sum _{k=1}^{n}c_{k}\varphi _{k}\), where \(\left\{ \varphi _{k}\right\} \) is a finite orthonormal system in \(L_2\) bounded in \(L_\infty \). No assumptions about smoothness of considered functions are required. Used technique relies only on the properties of Lorentz–Zygmund spaces and Fourier series map. In addition, real interpolation method is applied.

Keywords

Nikol’skii inequality Lorentz–Zygmund spaces orthonormal bounded system Fourier series 

Mathematics Subject Classification

41A17 42B05 42B35 42C05 

Notes

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Copyright information

© Sociedad Matemática Mexicana 2018

Authors and Affiliations

  1. 1.Fraunhofer Institute of Optronics, System Technologies and Image Exploitation IOSBEttlingenGermany

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