UMD Banach spaces and square functions associated with heat semigroups for Schrödinger and Laguerre operators

Abstract

In this paper we define square functions (also called Littlewood-Paley-Stein functions) associated with heat semigroups for Schrödinger and Laguerre operators acting on functions which take values in UMD Banach spaces. We extend classical (scalar) L^p-boundedness properties for the square functions to our Banach valued setting by using γ-radonifying operators. We also prove that these L^p-boundedness properties of the square functions actually characterize the Banach spaces having the UMD property.

References in corpus (5)

• Stochastic integration in UMD Banach spaces
• Conical square function estimates in UMD Banach spaces and applications to H-infinity functional calculi
• Square functions in the Hermite setting for functions with values in UMD spaces
• Characterization of UMD Banach spaces by imaginary powers of Hermite and Laguerre operators
• Weighted norm inequalities, spectral multipliers and Littlewood-Paley operators in the Schrödinger settings

Cited by in corpus (2)

• Vector valued multivariate spectral multipliers, Littlewood-Paley functions, and Sobolev spaces in hte Hermite setting
• Best constants in the vector-valued Littlewood-Paley-Stein theory