Lebesgue spaces with the variable rate of summability are considered in this work. Generalizations of Riesz and Paley theorems are proved in these spaces. The obtained results are applied, in particular, to a classical exponential system.
Riesz and Paley theorems, Fourier series, Lebesgue spaces with variable exponent, exponential system
"On Hausdorff-Young inequalities in generalized Lebesgue spaces,"
Turkish Journal of Mathematics: Vol. 44:
5, Article 18.
Available at: https://journals.tubitak.gov.tr/math/vol44/iss5/18