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arXiv · 1203.1480

Square functions in the Hermite setting for functions with values in UMD spaces

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

In this paper we characterize the Lebesgue Bochner spaces $L^p(\mathbb{R}^n,B)$, $1<p<\infty$, by using Littlewood-Paley $g$-functions in the Hermite setting, provided that $B$ is a UMD Banach space. We use $\gamma$-radonifying operators $\gamma (H,B)$ where $H=L^2((0,\infty),\frac{dt}{t})$. We also characterize the UMD Banach spaces in terms of $L^p(\mathbb{R}^n,B)$-$L^p(\mathbb{R}^n,\gamma (H,B))$ boundedness of Hermite Littlewood-Paley $g$-functions.

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Jorge J. Betancor, Alejandro J. Castro, Jezabel Curbelo, Juan C. Fariña, Lourdes Rodríguez-Mesa. 2012-03-07. Square functions in the Hermite setting for functions with values in UMD spaces. https://doi.org/10.1007/s10231-013-0335-9

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