This article is cited in 3 papers

The haar system as an unconditional basis in $L_p[0, 1]$

V. F. Gaposhkin


Abstract: We give a short proof of the known Paley–Marcinkiewicz theorem: the Haar system is an unconditional basis in $L_p$ ($p>1$). The method of proof consists in a simplification for the Haar system of the method applied in R. Gundy's and other authors' papers for similar problems of the general theory of martingales.

UDC: 517.5

Received: 24.04.1973

 English version: Mathematical Notes, 1974, 15:2, 108–111

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