Divergent Fourier series in function spaces near L1[0;1]

Bochkariev's theorem states that for any uniformly bounded orthonormal system Φ, there is a Lebesgue integrable function such the Fourier series of it with respect to Φ diverges on set positive measure. In this paper, we extended some class variable exponent spaces. We characterized spaces Lp(⋅)[0;1], 1<p(x)<∞ a.e. [0;1], above mentioned Bochkarev's valid.