On the approximation properties of Cesàro means of negative order of double Vilenkin – Fourier series
UDC 517.5 We establish approximation properties of Ces\`{a}ro $% (C,-\alpha ,-\beta)$ means with $\alpha ,\beta $ $\epsilon $ $(0,1)$ of Vilenkin\,--\,Fourier series. This result allows one to obtain a condition which is sufficient for the converge...
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| Date: | 2020 |
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| Main Authors: | , |
| Format: | Article |
| Language: | English |
| Published: |
Institute of Mathematics, NAS of Ukraine
2020
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| Online Access: | https://umj.imath.kiev.ua/index.php/umj/article/view/6045 |
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| Journal Title: | Ukrains’kyi Matematychnyi Zhurnal |
| Download file: |  |
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Ukrains’kyi Matematychnyi Zhurnal| Summary: | UDC 517.5
We establish approximation properties of Ces\`{a}ro $% (C,-\alpha ,-\beta)$ means with $\alpha ,\beta $ $\epsilon $ $(0,1)$ of Vilenkin\,--\,Fourier series. This result allows one to obtain a condition which is sufficient for the convergence of the means $\sigma _{n,m}^{-\alpha,-\beta }(x,y,f)$ to $f(x,y)$ in the $L^{p}$-metric. |
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| DOI: | 10.37863/umzh.v72i3.6045 |