Abstract
In this paper we consider Littlewood-Paley functions defined by the semigroups associated with the operator \(\mathcal {A}=-\frac {1}{2}{\Delta }-x\nabla \) in the inverse Gaussian setting for Banach valued functions. We characterize the uniformly convex and smooth Banach spaces by using \(L^{p}(\mathbb R^{n},\gamma _{-1})\)- properties of the \(\mathcal {A}\)-Littlewood-Paley functions. We also use Littlewood-Paley functions associated with \(\mathcal {A}\) to characterize the Köthe function spaces with the UMD property.
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Almeida, V., Betancor, J.J., Fariña, J.C. et al. Littlewood-Paley-Stein Theory and Banach Spaces in the Inverse Gaussian Setting. Potential Anal 59, 1235–1284 (2023). https://doi.org/10.1007/s11118-022-09993-w
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DOI: https://doi.org/10.1007/s11118-022-09993-w
Keywords
- Littlewood-Paley functions
- Inverse Gaussian measure
- q-uniformly convex
- q-uniformly smooth and UMD Banach spaces
- Köthe function spaces.