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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
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
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
Linking options:
https://www.mathnet.ru/eng/smj2803 https://www.mathnet.ru/eng/smj/v57/i5/p1021
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