A Decomposition for Hardy Martingales III
Paul F. X. M\"uller
TL;DR
This paper extends the theory of Hardy martingales by establishing Davis decompositions for vector-valued cases and demonstrating their applications, building upon prior work on scalar martingales.
Contribution
It introduces Davis decompositions for vector-valued Hardy martingales, advancing the understanding of their structure and inequalities.
Findings
Established Davis decompositions for vector-valued Hardy martingales
Illustrated applications of these decompositions in martingale inequalities
Extended previous scalar martingale results to vector-valued contexts
Abstract
We prove Davis decompositions for vector valued Hardy martingales and illustrate their use. This paper continues our previous work on Davis and Garsia inequalities for scalar Hardy martingales.
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