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Embedding theorems of function classes

B. Simonov·S. Tikhonov
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Abstract

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 $(λ,β)$-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.

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B. Simonov, S. Tikhonov. 2012-03-15. Embedding theorems of function classes. https://arxiv.org/abs/math/0506381

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