Relations for moduli of smoothness in various metrics: functions with restrictions on the Fourier coefficients

• M. K. Potapov ^[1] ; B. V. Simonov ^[2] ; Sergey Yu. Tikhonov ^[3]
  1. [1] Moscow State University

     Moscow State University

     Rusia

     
  2. [2] Volgograd State Technical University

     Volgograd State Technical University

     Rusia

     
  3. [3] ICREA and Centre de Recerca Matemàtica

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• Localización: Jaen journal on approximation, ISSN 1889-3066, ISSN-e 1989-7251, Vol. 1, Nº. 2, 2009, págs. 205-222
• Idioma: inglés
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• Resumen

  • We study the interrelation between different expressions which contain the moduli of smoothness in various metrics, ωα(f, t)p and ωβ(f, t)q. We consider functions represented by trigonometric series with some conditions on Fourier coefficients:

    namely with quasi-monotone and lacunary coefficients.