On the universal function for weighted spaces L^p_u[0,1], p>=1

TL;DR

This paper demonstrates the existence of a universal function in weighted L^p spaces on [0,1], capable of representing classes of functions via Fourier-Walsh series subseries, highlighting a unifying property across these spaces.

Contribution

It introduces a specific function that is universal for all weighted L^p spaces with p≥1, with respect to signs-subseries of its Fourier-Walsh series, a novel unifying result.

Findings

Existence of a universal function in weighted L^p spaces

Universal function works for all p≥1 with respect to Fourier-Walsh subseries

Highlights a unifying property across weighted L^p spaces

Abstract

In the paper it is shown that there exist a function g from L1[0,1] and a weight function 0<u(x)<=1, so that g is universal for each classes L^p_u[0,1], p>= 1 with respect to signs-subseries of its Fourier-Walsh series.