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Characterization of UMD Banach Spaces by Imaginary Powers of Hermite and Laguerre Operators |
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| Authors: | Jorge J. Betancor Alejandro J. Castro Jezabel Curbelo Lourdes Rodríguez-Mesa |
| Affiliation: | 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-UC3M-UCM), Consejo Superior de Investigaciones Científicas, Nicolás Cabrera 15, 28049, Madrid, Spain |
| Abstract: | In this paper we characterize the Banach spaces with the UMD property by means of L p -boundedness properties for the imaginary powers of the Hermite and Laguerre operators. In order to do this we need to obtain pointwise representations for the Laplace transform type multipliers associated with Hermite and Laguerre operators. |
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