What is it about?
Let X be a Banach function space. It is shown that the Burkholder-Davis-Gundy inequality is vaild in X if and only if X can be renormed so as to be rearragement-invariant and the lower Boyd index is (strictly) positive.
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Why is it important?
A complete characterization of a Banach function space in which the Burkholer-Davis-Gundy inequality to be valid is given.
Perspectives
To prove the main result, various ideas were needed.
Masato Kikuchi
University of Toyama
Read the Original
This page is a summary of: On the Davis inequality in Banach function spaces, Mathematische Nachrichten, May 2008, Wiley,
DOI: 10.1002/mana.200510635.
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