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A NECESSARY AND SUFFICIENT CONDITION FOR CERTAIN MARTINGALE INEQUALITIES IN BANACH FUNCTION SPACES

Published online by Cambridge University Press:  01 September 2007

MASATO KIKUCHI
MASATO KIKUCHI*
Affiliation:
Department of Mathematics, University of Toyama, 3190 Gofuku, Toyama 930-8555, Japan e-mail: [email protected]
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Abstract

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Let X be a Banach function space over a nonatomic probability space. We investigate certain martingale inequalities in X that generalize those studied by A. M. Garsia. We give necessary and sufficient conditions on X for the inequalities to be valid.

Keywords

60G4246E30
Type
Research Article
Information
Glasgow Mathematical Journal , Volume 49 , Issue 3 , September 2007 , pp. 431 - 447
Copyright
Copyright © Glasgow Mathematical Journal Trust 2007

References

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