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arXiv · 1404.5779

Conical square functions associated with Bessel, Laguerre and Schr\"odinger operators in UMD Banach spaces

Jorge J. Betancor·Alejandro J. Castro·Juan C. Fariña·Lourdes Rodríguez-Mesa
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Abstract

In this paper we consider conical square functions in the Bessel, Laguerre and Schr\"odinger settings where the functions take values in UMD Banach spaces. Following a recent paper of Hyt\"onen, van Neerven and Portal, in order to define our conical square functions, we use $\gamma$-radonifying operators. We obtain new equivalent norms in the Lebesgue-Bochner spaces $L^p((0,\infty ),\mathbb{B})$ and $L^p(\mathbb{R}^n,\mathbb{B})$, $1<p<\infty$, in terms of our square functions, provided that $\mathbb{B}$ is a UMD Banach space. Our results can be seen as Banach valued versions of known scalar results for square functions.

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Jorge J. Betancor, Alejandro J. Castro, Juan C. Fariña, Lourdes Rodríguez-Mesa. 2014-04-23. Conical square functions associated with Bessel, Laguerre and Schr\"odinger operators in UMD Banach spaces. https://doi.org/10.1016/j.jmaa.2016.10.006

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