The structure of universal functions for Lp-spaces, p ∈(0,1)

The paper sheds light on the structure of functions which are universal for L-p-spaces, p is an element of(0, 1), with respect to the signs of Fourier-Walsh coefficients. It is shown that there exists a measurable set E subset of [0, 1], whose measure is arbitrarily close to 1, such that by an appropriate change of values of any function f is an element of L-1 [0, 1] outside E a function (f) over tilde is an element of L-1 [0, 1] can be obtained that is universal for each L-p [0, 1]-space, p is an element of(0, 1), with respect to the signs of Fourier-Walsh coefficients.