Geodesic
Affine Walsh-type systems of functions in symmetric spaces
Sbornik. Mathematics, Tome 209 (2018) no. 4, pp. 469-490

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Affine Walsh-type systems of functions in symmetric spaces are investigated. It is shown that such a system can only be an unconditional basis in $L^2$. On the other hand the Besselian affine system generated by a function $f$ in the Zygmund-Orlicz space $\operatorname{Exp}L^p$, $p>0$, is an $\mathrm{RUC}$-system in a symmetric space $X$ if and only if $(\operatorname{Exp}L^q)^0\subset X\subset L^2$, where $(\operatorname{Exp}L^q)^0$ is the closure of $L^\infty$ in $\operatorname{Exp}L^q$ and $q=2p/(p+2)$. Bibliography: 20 titles.
Keywords: Walsh functions, Rademacher functions, Haar functions, symmetric space, Zygmund-Orlicz space. 
@article{SM_2018_209_4_a0,
     author = {S. V. Astashkin and P. A. Terekhin},
     title = {Affine {Walsh-type} systems of functions in symmetric spaces},
     journal = {Sbornik. Mathematics},
     pages = {469--490},
     publisher = {mathdoc},
     volume = {209},
     number = {4},
     year = {2018},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_2018_209_4_a0/}
}
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S. V. Astashkin; P. A. Terekhin. Affine Walsh-type systems of functions in symmetric spaces. Sbornik. Mathematics, Tome 209 (2018) no. 4, pp. 469-490. http://geodesic.mathdoc.fr/item/SM_2018_209_4_a0/