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arXiv · 1304.4018

Vector valued multivariate spectral multipliers, Littlewood-Paley functions, and Sobolev spaces in hte Hermite setting

J. J. Betancor·J. C. Fariña·A. Ssnabria
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Abstract

In this paper we find new equivalent norms in $L^p(\mathbb{R}^n,\mathbb{B})$ by using multivariate Littlewood-Paley functions associated with Poisson semigroup for the Hermite operator, provided that $\mathbb{B}$ is a UMD Banach space with the property ($\alpha$). We make use of $\gamma$-radonifying operators to get new equivalent norms that allow us to obtain $L^p(\mathbb{R}^n,\mathbb{B})$-boundedness properties for (vector valued) multivariate spectral multipliers for Hermite operators. As application of this Hermite multiplier theorem we prove that the Banach valued Hermite Sobolev and potential spaces coincide.

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J. J. Betancor, J. C. Fariña, A. Ssnabria. 2013-04-15. Vector valued multivariate spectral multipliers, Littlewood-Paley functions, and Sobolev spaces in hte Hermite setting. https://arxiv.org/abs/1304.4018

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