Rademacher functions in Nakano spaces

Abstract

The closed span of Rademacher functions is investigated in Nakano spaces $L^{p\left(\cdot \right)}$ 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 $L^{p\left(\cdot \right)}$ a basic sequence equivalent to the unit vector basis in ${\ell }_2$.