Universal series by trigonometric system in weighted $L^1_{\mu}$ spaces

TL;DR

This paper investigates the existence of trigonometric series that are universal in weighted L^1 spaces, meaning they can approximate any function through rearrangements or in the usual sense.

Contribution

It establishes conditions under which trigonometric series are universal in weighted L^1 spaces, extending previous results to these weighted contexts.

Findings

Existence of universal trigonometric series in weighted L^1 spaces.

Conditions for universality with respect to rearrangements.

Results applicable to both weighted and unweighted cases.

Abstract

In this paper we consider the question of existence of trigonometric series universal in weighted $L^1_{\mu}[0,2\pi]$ spaces with respect to rearrangements and in usual sense.