Geodesic
The structure of universal functions for $L^p$-spaces, $p\in(0,1)$
Sbornik. Mathematics, Tome 209 (2018) no. 1, pp. 35-55

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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, Walsh system, convergence in a metric.
Mots-clés : Fourier coefficients 
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     author = {M. G. Grigoryan and A. A. Sargsyan},
     title = {The structure of universal functions for $L^p$-spaces, $p\in(0,1)$},
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M. G. Grigoryan; A. A. Sargsyan. The structure of universal functions for $L^p$-spaces, $p\in(0,1)$. Sbornik. Mathematics, Tome 209 (2018) no. 1, pp. 35-55. http://geodesic.mathdoc.fr/item/SM_2018_209_1_a1/