Canad. Math. Bull. 42(1999), 321-334
Printed: Sep 1999
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.
martingale inequalities, rearrangement invariant function spaces
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.)