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

Research output: Contribution to journalArticle

1 Citation (Scopus)

Abstract

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
Volume447
Issue number1
DOIs
Publication statusPublished - Mar 1 2017

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Square Functions
Banach spaces
Friedrich Wilhelm Bessel
Mathematical operators
Banach space
Operator
Equivalent Norm
Lp Spaces
Stefan Banach
Scalar

Keywords

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

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

Cite this

Conical square functions associated with Bessel, Laguerre and Schrödinger operators in UMD Banach spaces. / Betancor, Jorge J.; Castro, Alejandro J.; Fariña, Juan C.; Rodríguez-Mesa, L.

In: Journal of Mathematical Analysis and Applications, Vol. 447, No. 1, 01.03.2017, p. 32-75.

Research output: Contribution to journalArticle

Betancor, Jorge J. ; Castro, Alejandro J. ; Fariña, Juan C. ; Rodríguez-Mesa, L. / Conical square functions associated with Bessel, Laguerre and Schrödinger operators in UMD Banach spaces. In: Journal of Mathematical Analysis and Applications. 2017 ; Vol. 447, No. 1. pp. 32-75.
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