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arXiv · 1209.4482

UMD Banach spaces and square functions associated with heat semigroups for Schr\"odinger and Laguerre operators

J. J. Betancor·A. J. Castro·J. C. Fariña·L. Rodríguez-Mesa
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Abstract

In this paper we define square functions (also called Littlewood-Paley-Stein functions) associated with heat semigroups for Schr\"odinger and Laguerre operators acting on functions which take values in UMD Banach spaces. We extend classical (scalar) L^p-boundedness properties for the square functions to our Banach valued setting by using \gamma-radonifying operators. We also prove that these L^p-boundedness properties of the square functions actually characterize the Banach spaces having the UMD property.

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J. J. Betancor, A. J. Castro, J. C. Fariña, L. Rodríguez-Mesa. 2012-09-20. UMD Banach spaces and square functions associated with heat semigroups for Schr\"odinger and Laguerre operators. https://doi.org/10.1002/mana.201400261

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