International Journal of Mathematics and Mathematical Sciences
Volume 2003 (2003), Issue 9, Pages 527-532
doi:10.1155/S0161171203206116
On vector-valued Hardy martingales and a generalized Jensen's inequality
Annela R. Kelly
and Brian P. Kelly
Department of Mathematics and Physics, University of Louisiana at Monroe, Monroe 71209, LA, USA
Abstract
We establish a generalized Jensen's inequality for analytic vector-valued functions on 𝕋N 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.