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Proceedings of the American Mathematical Society

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A martingale inequality related to exponential square integrability

Author: Jill Pipher
Journal: Proc. Amer. Math. Soc. 118 (1993), 541-546
MSC: Primary 42B25
MathSciNet review: 1131038
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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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