Composition of analytic paraproducts

Alexandru Aleman, Carme Cascante, Joan Fàbrega, Daniel Pascuas, José Ángel Peláez

Research output: Contribution to journalArticlepeer-review


For a fixed analytic function g on the unit disc D, we consider the analytic paraproducts induced by g, which are defined by Tgf(z)=∫0zf(ζ)g(ζ)dζ, Sgf(z)=∫0zf(ζ)g(ζ)dζ, and Mgf(z)=f(z)g(z). The boundedness of these operators on various spaces of analytic functions on D is well understood. The original motivation for this work is to understand the boundedness of compositions of two of these operators, for example Tg2,TgSg,MgTg, etc. Our methods yield a characterization of the boundedness of a large class of operators contained in the algebra generated by these analytic paraproducts acting on the classical weighted Bergman and Hardy spaces in terms of the symbol g. In some cases it turns out that this property is not affected by cancellation, while in others it requires stronger and more subtle restrictions on the oscillation of the symbol g than the case of a single paraproduct.

Original languageEnglish
Pages (from-to)293-319
JournalJournal des Mathematiques Pures et Appliquees
Early online date2021
Publication statusPublished - 2022

Subject classification (UKÄ)

  • Mathematics


  • Analytic paraproduct
  • Bloch space
  • BMOA space
  • Hardy spaces
  • Weighted Bergman spaces


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