Characterization of UMD Banach spaces by imaginary powers of Hermite and Laguerre operators

Abstract

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.

17 pages

References in corpus (1)

• Hankel Multipliers of Laplace Transform Type

Cited by in corpus (3)

• UMD Banach spaces and square functions associated with heat semigroups for Schrödinger and Laguerre operators
• Conical square functions associated with Bessel, Laguerre and Schrödinger operators in UMD Banach spaces
• Vector valued multivariate spectral multipliers, Littlewood-Paley functions, and Sobolev spaces in hte Hermite setting