Abstract
In this chapter we establish the Littlewood-Paley theorem for ℝ, Tand ℤ in the case of dyadic intervals and the corresponding dyadic partial sum operators. We present two approaches, one of which is, formally speaking, vectorial in nature, the other being partly scalar, partly vectorial. We also discuss the case of finite products of ℝ, Tand ℤ.
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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 ℝ, \(\mathbb{T}\) and ℤ: Dyadic Intervals. 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_8
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DOI: https://doi.org/10.1007/978-3-642-66366-6_8
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-66368-0
Online ISBN: 978-3-642-66366-6
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