The Littlewood-Paley Theorem for ℝ, \(\mathbb{T}\) and ℤ: Dyadic Intervals

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


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.


Trigonometric Polynomial Absolute Constant Weak Type Finite Product Dyadic Interval 
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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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