THE EXISTENCE OF FUNCTIONS WITH THE UNIVERSAL PROPERTY BY CHRESTENSON-LEVY SYSTEM

Abstract

In the present paper we will build a function , by strictly decreas­i­n­­g the Fourier Chrestenson-Levy coefficients  which has the universal property . In particular it is proved that there exists the function U ∈L¹[0, 1) so that for every p≥1 and each function  one can find a function , , such as .