Abstract
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.
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© 1977 Springer-Verlag Berlin Heidelberg
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Edwards, R.E., Gaudry, G.I. (1977). The Littlewood-Paley Theorem for Certain Disconnected Groups. In: Littlewood-Paley and Multiplier Theory. Ergebnisse der Mathematik und ihrer Grenzgebiete, vol 90. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-66366-6_5
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DOI: https://doi.org/10.1007/978-3-642-66366-6_5
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-66368-0
Online ISBN: 978-3-642-66366-6
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