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

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  • Annela R. Kelly
  • Brian P. Kelly

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.

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  • Annela R. Kelly & Brian P. Kelly, 2003. "On vector-valued Hardy martingales and a generalized Jensen's inequality," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2003, pages 1-6, January.
    • Handle: RePEc:hin:jijmms:379217
    DOI: 10.1155/S0161171203206116
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