A martingale inequality related to exponential square integrability

Pipher, Jill

doi:10.1090/S0002-9939-1993-1131038-3

A martingale inequality related to exponential square integrability
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by Jill Pipher

Proc. Amer. Math. Soc. 118 (1993), 541-546

DOI: https://doi.org/10.1090/S0002-9939-1993-1131038-3

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Abstract:

We present an inequality for dyadic martingales (together with its continuous analog for functions on ${\mathbb {R}^n}$) which is shown to be equivalent to a result of Chang-Wilson-Wolff on exponential square integrability. The analog of this weighted inequality for double dyadic martingales is also proven. Finally, we discuss a possible connection between these inequalities and a theorem of Garnett.

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