Vol. 9, No. 1, 2016

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Sergey Astashkin and Mieczysław Mastyło

Vol. 9 (2016), No. 1, 1–14
DOI: 10.2140/apde.2016.9.1
Abstract

The closed span of Rademacher functions is investigated in Nakano spaces ${L}^{p\left(\phantom{\rule{0.3em}{0ex}}\cdot \phantom{\rule{0.3em}{0ex}}\right)}$ on $\left[0,1\right]$ equipped with the Lebesgue measure. The main result of this paper states that under some conditions on distribution of the exponent function $p$ the Rademacher functions form in ${L}^{p\left(\phantom{\rule{0.3em}{0ex}}\cdot \phantom{\rule{0.3em}{0ex}}\right)}$ a basic sequence equivalent to the unit vector basis in ${\ell }_{2}$.

Keywords
Rademacher functions, Nakano spaces, symmetric spaces
Mathematical Subject Classification 2010
Primary: 46E30
Secondary: 46B20, 46B42