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

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 \(\gamma\)-rad...

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Published in:arXiv.org 2014-09
Main Authors: Betancor, J J, Fariña, J C, Ssnabria, A
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Language:English
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Banach spaces
Equivalence
Multipliers
Norms
Operators
Sobolev space
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description 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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subjects Banach spaces
Equivalence
Multipliers
Norms
Operators
Sobolev space
title Vector valued multivariate spectral multipliers, Littlewood-Paley functions, and Sobolev spaces in hte Hermite setting
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