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Inverse Jackson theorems in spaces with integral metric

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Ukrainian Mathematical Journal Aims and scope

In the spaces L ψ(T) of periodic functions with metric

$$ \rho {\left( {f,0} \right)_\psi } = \int\limits_T {\psi \left( {\left| {f(x)} \right|} \right)dx,} $$

where ψ is a function of the modulus-of-continuity type, we investigate the inverse Jackson theorems in the case of approximation by trigonometric polynomials. It is proved that an inverse Jackson theorem is true if and only if the lower dilation exponent of the function ψ is not equal to zero.

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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 64, No. 3, pp. 351–362, March, 2012.

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Pichugov, S.A. Inverse Jackson theorems in spaces with integral metric. Ukr Math J 64, 394–407 (2012). https://doi.org/10.1007/s11253-012-0654-9

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  • DOI: https://doi.org/10.1007/s11253-012-0654-9

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