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 $A=−12Δ−x∇in the inverse Gaussian setting for Banach valued functions. We characterize the uniformly convex and smooth Banach spaces by using$L^{p}(\mathbb R^{n},\gamma _{-1})$Lp(ℝn,γ−1)- properties of the$\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.
Publisher
Springer Science and Business Media LLC
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