Generalization of a theorem on Besov-Nikol'skiĭ classes
The author introduces a class of sequences, the so-called class of rest bounded second variation sequences. He proves that this space is wider than the known classes of quasi-monotone sequences and of rest bounded variation sequences. Known criteria, in terms of the sequence of the Fourier coefficients to be in such classes along with some other conditions for belonging of a function from \(L^p,\) \(1<p<\infty,\) to the Besov-Nikol'skiĭ class are extended to the above new space of sequences. The author starts from results due to Leindler and due to Tikhonov. However, one more paper by \textit{S. Tikhonov} should be added: [J. Math. Anal. Appl. 326, No.~1, 721--735 (2007; Zbl 1106.42003)]; further extensions of sequence classes are given in it which are applicable to the considered problem and related ones.
scientific article; zbMATH DE number 5848554
scientific article