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Hardy spaces on ZN

Published online by Cambridge University Press:  12 July 2007

Santiago Boza  and
María J. Carro
Santiago Boza
Affiliation:
Departament de Matemàtica Aplicada IV, EUPVG Avda. Victor Balaguer s/n, 08800 Vilanova I Geltrú, Spain (boza@mat.upc.es)
María J. Carro
Affiliation:
Departament de Matemàtica Aplicada i Anàlisi, Universitat de Barcelona, 08071 Barcelona, Spain (carro@cerber.mat.ub.es)
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Abstract

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The work of Coifman and Weiss concerning Hardy spaces on spaces of homogeneous type gives, as a particular case, a definition of Hp(ZN) in terms of an atomic decomposition.

Other characterizations of these spaces have been studied by other authors, but it was an open question to see if they can be defined, as it happens in the classical case, in terms of a maximal function or via the discrete Riesz transforms.

In this paper, we give a positive answer to this question.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 132 , Issue 1 , February 2002 , pp. 25 - 43
Copyright
Copyright © Royal Society of Edinburgh 2002