A remark on the multipliers of the Haar basis of $L^1[0,1]$
Volume 227 / 2015
Studia Mathematica 227 (2015), 141-148
MSC: Primary 46B03; Secondary 46E30, 42C10.
DOI: 10.4064/sm227-2-4
Abstract
A proof of a necessary and sufficient condition for a sequence to be a multiplier of the normalized Haar basis of $L^1 [0, 1]$ is given. This proof depends only on the most elementary properties of this system and is an alternative proof to that recently found by Semenov \& Uksusov (2012). Additionally, representations are given, which use stochastic processes, of this multiplier norm and of related multiplier norms.
