Complex Analysis and Operator Theory

, Volume 7, Issue 4, pp 1019–1048 | Cite as

Characterization of UMD Banach Spaces by Imaginary Powers of Hermite and Laguerre Operators

  • Jorge J. Betancor
  • Alejandro J. Castro
  • Jezabel Curbelo
  • Lourdes Rodríguez-MesaEmail author


In this paper we characterize the Banach spaces with the UMD property by means of L p -boundedness properties for the imaginary powers of the Hermite and Laguerre operators. In order to do this we need to obtain pointwise representations for the Laplace transform type multipliers associated with Hermite and Laguerre operators.


Laguerre operator Laplace transform type multipliers UMD spaces Imaginary powers 

Mathematics Subject Classification (2010)

42C05 (primary) 42C15 (secondary) 


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Copyright information

© Springer Basel AG 2011

Authors and Affiliations

  • Jorge J. Betancor
    • 1
  • Alejandro J. Castro
    • 1
  • Jezabel Curbelo
    • 2
  • Lourdes Rodríguez-Mesa
    • 1
    Email author
  1. 1.Departamento de Análisis MatemáticoUniversidad de la LagunaLa Laguna (Sta. Cruz de Tenerife)Spain
  2. 2.Instituto de Ciencias Matemáticas (CSIC-UAM-UC3M-UCM), Consejo Superior de Investigaciones CientíficasMadridSpain

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