On the universal function for weighted spaces Lμp[0,1], p≥1

Abstract

In this article, we show that there exist a function $g\in L^1[0,1]$ and a weight function $0<\mu \left(x\right)\le 1$ so that $g$ is universal for each class $L_{\mu }^p[0,1]$, $p\ge 1$, with respect to signs-subseries of its Fourier–Walsh series.