Mathematics – Classical Analysis and ODEs
Scientific paper
2005-06-19
Mathematics
Classical Analysis and ODEs
34 pages, final version, Sbornik: Mathematics
Scientific paper
In this paper we obtain the necessary and sufficient conditions for embedding results of different function classes. The main result is a criterion for embedding theorems for the so-called generalized Weyl-Nikol'skii class and the generalized Lipschitz class. To define the Weyl-Nikol'skii class, we use the concept of a $(\lambda,\beta)$-derivative, which is a generalization of the derivative in the sense of Weyl. As corollaries, we give estimates of norms and moduli of smoothness of transformed Fourier series.
Simonov B. B.
Tikhonov S.
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