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Sibirskii Matematicheskii Zhurnal, 2016, Volume 57, Number 5, Pages 1021–1035
DOI: https://doi.org/10.17377/smzh.2016.57.508
(Mi smj2803)
 

This article is cited in 2 scientific papers (total in 2 papers)

On existence of a universal function for $L^p[0,1]$ with $p\in(0,1)$

M. G. Grigoryana, A. A. Sargsyanb

a Yerevan State University, Yerevan, Armenia
b Synchrotron Research Institute CANDLE, Yerevan, Armenia
Full-text PDF (335 kB) Citations (2)
References:
Abstract: We show that, for every number $p\in(0,1)$, there is $g\in L^1[0,1]$ (a universal function) that has monotone coefficients $c_k(g)$ and the Fourier–Walsh series convergent to $g$ (in the norm of $L^1[0,1]$) such that, for every $f\in L^p[0,1]$, there are numbers $\delta_k=\pm1,0$ and an increasing sequence of positive integers $N_q$ such that the series $\sum^{+\infty}_{k=0}\delta_kc_k(g)W_k$ (with $\{W_k\}$ the Walsh system) and the subsequence $\sigma^{(\alpha)}_{N_q}$, $\alpha\in(-1,0)$, of its Cesáro means converge to $f$ in the metric of $L^p[0,1]$.
Keywords: universal function, Fourier coefficient, Walsh system, convergence in a metric.
Received: 21.04.2015
English version:
Siberian Mathematical Journal, 2016, Volume 57, Issue 5, Pages 796–808
DOI: https://doi.org/10.1134/S0037446616050086
Bibliographic databases:
Document Type: Article
UDC: 517.51
Language: Russian
Citation: M. G. Grigoryan, A. A. Sargsyan, “On existence of a universal function for $L^p[0,1]$ with $p\in(0,1)$”, Sibirsk. Mat. Zh., 57:5 (2016), 1021–1035; Siberian Math. J., 57:5 (2016), 796–808
Citation in format AMSBIB
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\paper On existence of a~universal function for $L^p[0,1]$ with~$p\in(0,1)$
\jour Sibirsk. Mat. Zh.
\yr 2016
\vol 57
\issue 5
\pages 1021--1035
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\crossref{https://doi.org/10.17377/smzh.2016.57.508}
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\issue 5
\pages 796--808
\crossref{https://doi.org/10.1134/S0037446616050086}
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  • This publication is cited in the following 2 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    Сибирский математический журнал Siberian Mathematical Journal
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