Sharp inequalities for the Haar system and martingale transforms

  1. Adam Osękowski


A classical result of Paley and Marcinkiewicz asserts that the Haar system on [0; 1] forms an unconditional basis in Lp provided 1 < p < ∞. The purpose of the paper is to study related weak-type inequalities, which can be regarded as a version of this property for p = 1. Probabilistic counterparts, leading to some sharp estimates for martingale transforms, are presented.

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Probability and Mathematical Statistics

36, z. 1, 2016

Pages from 147 to 164

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