Inverse Jackson theorems in spaces with integral metric
In the spaces $L_{\Psi}(T)$ of periodic functions with metric $\rho(f, 0)_{\Psi} = \int_T \Psi(|f(x)|)dx$, where $\Psi$ 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 the inver...
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| Date: | 2012 |
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| Main Authors: | , |
| Format: | Article |
| Language: | Russian English |
| Published: |
Institute of Mathematics, NAS of Ukraine
2012
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| Online Access: | https://umj.imath.kiev.ua/index.php/umj/article/view/2581 |
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| Journal Title: | Ukrains’kyi Matematychnyi Zhurnal |
| Download file: |  |
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Ukrains’kyi Matematychnyi Zhurnal| Summary: | In the spaces $L_{\Psi}(T)$ of periodic functions with metric $\rho(f, 0)_{\Psi} = \int_T \Psi(|f(x)|)dx$, where $\Psi$ 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 the inverse Jackson theorem is true if and only if the lower dilation exponent of the function $\Psi$ is not equal to zero. |
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