On Vector-valued Hardy Martingales and a Generalized Jensen’s Inequality
نویسندگان
چکیده
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.
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