Characterization of UMD Banach spaces by imaginary powers of Hermite and   Laguerre operators
  In this paper we characterize the Banach spaces with the UMD property by means of Lp-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. 
Jorge J. Betancor, Alejandro J. Castro, Jezabel Curbelo, Lourdes   Rodr\'iguez-Mesa
math.CA