Random sums

  • Tuomas Hytönen
  • Jan van Neerven
  • Mark Veraar
  • Lutz Weis
Chapter
Part of the Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics book series (MATHE3, volume 67)

Abstract

One of the main themes in these volumes is the use of probabilistic techniques in general, and random sums in particular, in Banach space-valued Analysis. A first glimpse of their usefulness was already offered by the classical Theorem 2.1.9 of Paley, Marcinkiewicz and Zygmund on the extendability of bounded operators on \( L^{p} \left( S \right) \) to bounded operators on \( L^{p} \left( {S;H} \right) \), the proof of which involved estimates on Gaussian random sums. On the other hand, Rademacher random sums played a key role both in the formulation and in the proofs of the Littlewood–Paley theory in \( L^{p} \left( {{\mathbb{R}}^{d} ;X} \right) \) developed in Chapter  5.

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Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  • Tuomas Hytönen
    • 1
  • Jan van Neerven
    • 2
  • Mark Veraar
    • 3
  • Lutz Weis
    • 4
  1. 1.Department of Mathematics and StatisticsUniversity of HelsinkiHelsinkiFinland
  2. 2.Delft Institute of Applied MathematicsDelft University of TechnologyDelftThe Netherlands
  3. 3.Delft Institute of Applied MathematicsDelft University of TechnologyDelftThe Netherlands
  4. 4.Department of MathematicsKarlsruhe Institute of TechnologyKarlsruheGermany

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