What is it about?
It is well kown a submartingale can be decomposed into the sum of a martingale and an increasing process. In ths paper, necesaary and sufficient condtions for some inequalities involving processes appearing in the Doob decompostion of a submaringale are given.
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Why is it important?
Not only sufficient conditions but also necessary conditions are given.
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This page is a summary of: On some inequalities for Doob decompositions in Banach function spaces, Mathematische Zeitschrift, May 2009, Springer Science + Business Media,
DOI: 10.1007/s00209-009-0546-3.
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