On vector-valued Hardy martingales and a generalized Jensen's inequality

Annela R. Kelly and Brian P. Kelly

International Journal of Mathematics and Mathematical Sciences, 2003, vol. 2003, 1-6

Abstract:

We establish a generalized Jensen's inequality for analytic vector-valued functions on 𝕋 N using a monotonicity property of vector-valued Hardy martingales. We then discuss how this result extends to functions on a compact abelian group G , which are analytic with respect to an order on the dual group. We also give a generalization of Helson and Lowdenslager's version of Jensen's inequality to certain operator-valued analytic functions.

Date: 2003
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:379217

DOI: 10.1155/S0161171203206116

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