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Hardy Martingales and Jensen's inequality

Published online by Cambridge University Press:  17 April 2009

NakhlĂ© H. Asmar  and
Stephen J. Montgomery-Smith
Nakhlé H. Asmar
Affiliation:
Department of Mathematics, University of Missouri-Columbia, Columbia, MI 65211, United States of America
Stephen J. Montgomery-Smith
Affiliation:
Department of Mathematics, University of Missouri-Columbia, Columbia, MI 65211, United States of America
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Hardy martingales were introduced by Garling and used to study analytic functions on the N-dimensional torus 𝕋N, where analyticity is defined using a lexicographic order on the dual group â„€N. We show how, by using basic properties of orders on â„€N, we can apply Garling's method in the study of analytic functions on an arbitrary compact Abelian group with an arbitrary order on its dual group. We illustrate our approach by giving a new and simple proof of a famous generalised Jensen's Inequality due to Helson and Lowdenslager[5].

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 55 , Issue 2 , April 1997 , pp. 185 - 195
Copyright
Copyright © Australian Mathematical Society 1997

References

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