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.


42A16 Fourier coefficients, Fourier series of functions with special properties, special Fourier series
Full Text: arXiv