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 martingale inequalities, rearrangement invariant function spaces

MSC Classifications:

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