Almost everywhere convergence of Cesàro means of two variable Walsh – Fourier series with varying parameteres
UDC 517.5 We prove that the maximal operator of some $(C , \beta_{n})$ means of cubical partial sums of two variable Walsh – Fourier series of integrable functions is of weak type $(L_1,L_1)$. Moreover, the $ (C , \beta_{n})$-means $\sigma_{2^n}^{\beta_{n}} f$ of the function $ f \in L_{1} $ converg...
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| Datum: | 2021 |
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| Hauptverfasser: | , , |
| Format: | Artikel |
| Sprache: | Englisch |
| Veröffentlicht: |
Institute of Mathematics, NAS of Ukraine
2021
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| Online Zugang: | https://umj.imath.kiev.ua/index.php/umj/article/view/196 |
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| Назва журналу: | Ukrains’kyi Matematychnyi Zhurnal |
| Завантажити файл: |  |
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Ukrains’kyi Matematychnyi Zhurnal| Zusammenfassung: | UDC 517.5
We prove that the maximal operator of some $(C , \beta_{n})$ means of cubical partial sums of two variable Walsh – Fourier series of integrable functions is of weak type $(L_1,L_1)$. Moreover, the $ (C , \beta_{n})$-means $\sigma_{2^n}^{\beta_{n}} f$ of the function $ f \in L_{1} $ converge a.e. to $f$ for $ f \in L_{1}(I^2) $, where $I$ is the Walsh group for some sequences $1> \beta_n\searrow 0$. |
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| DOI: | 10.37863/umzh.v73i3.196 |