Embedding theorems in constructive approximation

B. V. Simonov   ; S. Yu. Tikhonov

Sbornik. Mathematics, Tome 199 (2008) no. 9, pp. 1367-1407

Résumé

Necessary and sufficient conditions for the accuracy of embedding theorems of various function classes are obtained. The main result of the paper is a criterion for embeddings between generalized Weyl-Nikol'skiǐ and generalized Lipschitz classes. To define the Weyl-Nikol'skiǐ classes we use the concept of a $(\lambda,\beta)$-derivative, which is a generalization of the derivative in the sense of Weyl. As corollaries, estimates for the norms and moduli of smoothness of transformed Fourier series are obtained. Bibliography: 59 titles.

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