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 Mat. Sb., 2008, Volume 199, Number 9, Pages 107–148 (Mi msb3941)

Embedding theorems in constructive approximation

B. V. Simonova, S. Yu. Tikhonovbc

b Scuola Normale Superiore in Pisa
c Institució Catalana de Recerca i Estudis Avancats

Abstract: 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.
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DOI: https://doi.org/10.4213/sm3941

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English version:
Sbornik: Mathematics, 2008, 199:9, 1367–1407

Bibliographic databases:

UDC: 517.518.23+517.518.83
MSC: Primary 46E35, 26A33, 41A17; Secondary 26A16, 42A45

Citation: B. V. Simonov, S. Yu. Tikhonov, “Embedding theorems in constructive approximation”, Mat. Sb., 199:9 (2008), 107–148; Sb. Math., 199:9 (2008), 1367–1407

Citation in format AMSBIB
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