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
Externally publishedYes

Fingerprint

BMO Space
Hardy Space
Hermite
Operator
Banach space
Denote
Hermite Functions
Equivalent Norm
Square Functions
Bounded Operator
Siméon Denis Poisson
Semigroup
Hilbert space

Keywords

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

ASJC Scopus subject areas

  • Analysis

Cite this

γ-Radonifying operators and UMD-valued Littlewood-Paley-Stein functions in the Hermite setting on BMO and Hardy spaces. / Betancor, J. J.; Castro, A. J.; Curbelo, J.; Fariña, J. C.; Rodríguez-Mesa, L.

In: Journal of Functional Analysis, Vol. 263, No. 12, 15.12.2012, p. 3804-3856.

Research output: Contribution to journalArticle

Betancor, J. J. ; Castro, A. J. ; Curbelo, J. ; Fariña, J. C. ; Rodríguez-Mesa, L. / γ-Radonifying operators and UMD-valued Littlewood-Paley-Stein functions in the Hermite setting on BMO and Hardy spaces. In: Journal of Functional Analysis. 2012 ; Vol. 263, No. 12. pp. 3804-3856.
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