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Averaging Operators and Martingale Inequalities in Rearrangement Invariant Function Spaces

Published online by Cambridge University Press:  20 November 2018

Masato Kikuchi
Masato Kikuchi*
Affiliation:
Department of Mathematics Toyama University 3190 Gofuku Toyama 930-8555 Japan, email: kikuchi@sci.toyama-u.ac.jp
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Abstract

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We shall study some connection between averaging operators and martingale inequalities in rearrangement invariant function spaces. In Section 2 the equivalence between Shimogaki’s theorem and some martingale inequalities will be established, and in Section 3 the equivalence between Boyd’s theorem and martingale inequalities with change of probability measure will be established.

Keywords

60G4460G4646E30Martingale inequalitiesrearrangement invariant function spaces
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 42 , Issue 3 , 01 September 1999 , pp. 321 - 334
Copyright
Copyright © Canadian Mathematical Society 1999

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