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# Averaging Operators and Martingale Inequalities in Rearrangement Invariant Function Spaces

Published:1999-09-01
Printed: Sep 1999
• Masato Kikuchi
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## Abstract

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: martingale inequalities, rearrangement invariant function spaces
 MSC Classifications: 60G44 - Martingales with continuous parameter 60G46 - Martingales and classical analysis 46E30 - Spaces of measurable functions ($L^p$-spaces, Orlicz spaces, Kothe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.)

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