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Square functions in the Hermite setting for functions with values in UMD spaces |
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| Authors: | J J Betancor A J Castro J Curbelo J C Fariña L Rodríguez-Mesa |
| Institution: | 1. Departamento de Análisis Matemático, Universidad de la Laguna, Campus de Anchieta, Avda. Astrofísico Francisco Sánchez, s/n, 38271, La Laguna (Sta. Cruz de Tenerife), Spain 2. Instituto de Ciencias Matemáticas (CSIC-UAM-UCM-UC3M), Nicolás Cabrera, 13-15, 28049, Madrid, Spain 3. Departamento de Matemáticas, Facultad de Ciencias, Universidad Autónoma de Madrid, 28049, Madrid, Spain |
| Abstract: | In this paper, we characterize the Lebesgue Bochner spaces \(L^p({\mathbb{R }}^{n},B),\, 1 , 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 \(H=L^2((0,\infty ),\frac{\mathrm{d}t}{t})\) . 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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