Littlewood-Paley-Stein Theory and Banach Spaces in the Inverse Gaussian Setting

Author:

Almeida Víctor,Betancor Jorge J.,Fariña Juan C.,Rodríguez-Mesa LourdesORCID

Abstract

AbstractIn this paper we consider Littlewood-Paley functions defined by the semigroups associated with the operator$\mathcal {A}=-\frac {1}{2}{\Delta }-x\nabla $A=12Δxin the inverse Gaussian setting for Banach valued functions. We characterize the uniformly convex and smooth Banach spaces by using$L^{p}(\mathbb R^{n},\gamma _{-1})$Lp(n,γ1)- properties of the$\mathcal {A}$A-Littlewood-Paley functions. We also use Littlewood-Paley functions associated with$\mathcal {A}$Ato characterize the Köthe function spaces with the UMD property.

Funder

Universidad de la Laguna

Publisher

Springer Science and Business Media LLC

Subject

Analysis

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