γ-Radonifying operators and UMD-valued Littlewood-Paley-Stein functions in the Hermite setting on BMO and Hardy spaces

J. J. Betancor, A. J. Castro, J. Curbelo, J. C. Fariña, L. Rodríguez-Mesa

Research output: Contribution to journalArticle

4 Citations (Scopus)

Abstract

In this paper we study Littlewood-Paley-Stein functions associated with the Poisson semigroup for the Hermite operator on functions with values in a UMD Banach space B. If we denote by H the Hilbert space L 2((0, ∞), dt/t), γ(H,B) represents the space of γ-radonifying operators from H into B. We prove that the Hermite square function defines bounded operators from BMO L(R n,B) (respectively, H L 1(R n,B)) into BMO L(R n,γ(H,B)) (respectively, H L 1(R n,γ(H,B))), where BMO L and H L 1 denote BMO and Hardy spaces in the Hermite setting. Also, we obtain equivalent norms in BMO L(R n,B) and H L 1(R n,B) by using Littlewood-Paley-Stein functions. As a consequence of our results, we establish new characterizations of the UMD Banach spaces.

Original languageEnglish
Pages (from-to)3804-3856
Number of pages53
JournalJournal of Functional Analysis
Volume263
Issue number12
DOIs
Publication statusPublished - Dec 15 2012

Keywords

  • BMO
  • Hardy spaces
  • Hermite operator
  • Littlewood-Paley-Stein functions
  • UMD Banach spaces
  • γ-Radonifying operators

ASJC Scopus subject areas

  • Analysis

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