The Littlewood-Paley Theorem for Certain Disconnected Groups

Part of the Ergebnisse der Mathematik und ihrer Grenzgebiete book series (MATHE2, volume 90)


The first theorem of the type we are about to discuss was discovered by Paley [31]. It is a theorem about Walsh series or, equivalently, about Fourier series on the Cantor group D2. In Appendix C we give a brief discussion of the relationship between Fourier analysis on the Cantor group and the theory of Walsh series on [0, 1]. Here now are a description and a proof of Paley’s theorem in the setting of harmonic analysis on D2.


Haar Measure Dual Group Compact Abelian Group Open Subgroup Neighbourhood Base 
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Copyright information

© Springer-Verlag Berlin Heidelberg 1977

Authors and Affiliations

  1. 1.Institute of Advanced StudiesAustralian National UniversityCanberraAustralia
  2. 2.Flinders UniversityBedford ParkAustralia

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