Geodesic
Averaging Operators and Martingale Inequalities in Rearrangement Invariant Function Spaces
Canadian mathematical bulletin, Tome 42 (1999) no. 3, pp. 321-334

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DOI

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.
DOI : 10.4153/CMB-1999-038-7
Mots-clés : 60G44, 60G46, 46E30, Martingale inequalities, rearrangement invariant function spaces 
Kikuchi, Masato. Averaging Operators and Martingale Inequalities in Rearrangement Invariant Function Spaces. Canadian mathematical bulletin, Tome 42 (1999) no. 3, pp. 321-334. doi: 10.4153/CMB-1999-038-7
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     author = {Kikuchi, Masato},
     title = {Averaging {Operators} and {Martingale} {Inequalities} in {Rearrangement} {Invariant} {Function} {Spaces}},
     journal = {Canadian mathematical bulletin},
     pages = {321--334},
     year = {1999},
     volume = {42},
     number = {3},
     doi = {10.4153/CMB-1999-038-7},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1999-038-7/}
}
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