Conical square functions associated with Bessel, Laguerre and Schrödinger operators in UMD Banach spaces

Jorge J. Betancor, Alejandro J. Castro, Juan C. Fariña, L. Rodríguez-Mesa

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In this paper we consider conical square functions in the Bessel, Laguerre and Schrödinger settings where the functions take values in UMD Banach spaces. Following a recent paper of Hytönen, van Neerven and Portal [36], in order to define our conical square functions, we use γ-radonifying operators. We obtain new equivalent norms in the Lebesgue–Bochner spaces Lp((0,∞),B) and Lp(Rn,B), 1<p<∞, in terms of our square functions, provided that B is a UMD Banach space. Our results can be seen as Banach valued versions of known scalar results for square functions.

Original languageEnglish
Pages (from-to)32-75
Number of pages44
JournalJournal of Mathematical Analysis and Applications
Issue number1
Publication statusPublished - Mar 1 2017



  • Bessel
  • Conical square functions
  • Laguerre
  • Schrödinger
  • UMD Banach spaces
  • Vector-valued harmonic analysis

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

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