A theorem on Besov-Nikol'skiǐ class

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Abstract

Very recently S. Yu. Tikhonov proved a theorem which gives a necessary and sufficient condition in order that a function f(x) ∈ L p having quasi-monotone decreasing Fourier coefficients should belong to the Besov-Nikol'skiǐ class. In the present paper the analogue of his result is proved with function having Fourier coefficients of rest bounded variation.

Original languageEnglish
Pages (from-to)237-248
Number of pages12
JournalPublicationes Mathematicae
Volume64
Issue number1-2
Publication statusPublished - Mar 19 2004

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Keywords

  • Besov-Nikol'skiǐ class
  • Fourier coefficients
  • Inequalities for sums
  • Modulus of smoothness
  • Sequences of monotone type

ASJC Scopus subject areas

  • Mathematics(all)

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