International Journal of Mathematics and Mathematical Sciences
Volume 2003 (2003), Issue 9, Pages 527-532
On vector-valued Hardy martingales and a generalized Jensen's inequality
Department of Mathematics and Physics, University of Louisiana at Monroe, Monroe 71209, LA, USA
Received 24 June 2002
Copyright © 2003 Annela R. Kelly and Brian P. Kelly. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
We establish a generalized Jensen's inequality for analytic vector-valued functions on using a monotonicity
property of vector-valued Hardy martingales. We then discuss how this
result extends to functions on a compact abelian group , 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.