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A remark on the multipliers of the Haar basis of $L^1[0,1]$

Volume 227 / 2015

H. M. Wark Studia Mathematica 227 (2015), 141-148 MSC: Primary 46B03; Secondary 46E30, 42C10. DOI: 10.4064/sm227-2-4


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.


  • H. M. Wark9 Westwood Terrace, South Bank
    York, North Yorkshire, England
    United Kingdom, YO23 1HJ

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