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On monotone Fourier coefficients of a function belonging to Nikol’skij-Besov classes. (English) Zbl 1013.42002
The authors give a necessary and sufficient condition for a function $$f\in L^p$$ ($$1<p<\infty$$) with the Fourier series $$\sum_{n\geq 0}a_n\cos nx$$, ($$a_n\downarrow 0$$) to be in the Nikol’skij-Besov class in terms of its coefficients.

##### MSC:
 42A16 Fourier coefficients, Fourier series of functions with special properties, special Fourier series
##### Keywords:
Nikol’skij-Besov class; Fourier series