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This article is cited in 15 scientific papers (total in 15 papers)
The structure of universal functions for $L^p$-spaces, $p\in(0,1)$
M. G. Grigoryana, A. A. Sargsyanb a Yerevan State University, Armenia
b Russian-Armenian (Slavonic) State University, Yerevan, Armenia
Abstract:
The paper sheds light on the structure of functions which are universal for $L^p$-spaces, $p\in(0,1)$, with respect to the signs of Fourier-Walsh coefficients. It is shown that there exists a measurable set $E\subset [0,1]$, whose measure is arbitrarily close to $1$, such that by an appropriate change of values of any function $f\in L^1[0,1]$ outside $E$ a function $\widetilde f\in L^1[0,1]$ can be obtained that is universal for each $L^p[0,1]$-space, $p\in(0,1)$, with respect to the signs of Fourier-Walsh coefficients.
Bibliography: 28 titles.
Keywords:
universal function, Fourier coefficients, Walsh system, convergence in a metric.
Received: 27.08.2016 and 27.01.2017
Citation:
M. G. Grigoryan, A. A. Sargsyan, “The structure of universal functions for $L^p$-spaces, $p\in(0,1)$”, Mat. Sb., 209:1 (2018), 37–57; Sb. Math., 209:1 (2018), 35–55
Linking options:
https://www.mathnet.ru/eng/sm8806https://doi.org/10.1070/SM8806 https://www.mathnet.ru/eng/sm/v209/i1/p37
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Abstract page: | 626 | Russian version PDF: | 56 | English version PDF: | 12 | References: | 60 | First page: | 32 |
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