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arXiv · 2102.13381

Littlewood-Paley-Stein theory and Banach spaces in the inverse Gaussian setting

V. Almeida·J. J. Betancor·J. C. Fariña·L. Rodríguez-Mesa
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Abstract

In this paper we consider Littlewood-Paley functions defined by the semigroups associated with the operator $\mathcal{A}=-\frac{\Delta}{2}-x\nabla$ 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 K\"othe function spaces with the UMD property.

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BibTeXRIS

V. Almeida, J. J. Betancor, J. C. Fariña, L. Rodríguez-Mesa. 2021-02-26. Littlewood-Paley-Stein theory and Banach spaces in the inverse Gaussian setting. https://arxiv.org/abs/2102.13381

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