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UMD Banach spaces and the maximal regularity for the square root of several operators

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Abstract

In this paper we prove that the maximal L p-regularity property on the interval (0,T), T>0, for Cauchy problems associated with the square root of Hermite, Bessel or Laguerre type operators on L 2(Ω,dμ;X), characterizes the UMD property for the Banach space X.

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Acknowledgements

We would like to offer thanks to the referee for his advice which have improved quite a lot this paper.

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Authors and Affiliations

  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

    Victor Almeida, Jorge J. Betancor & Alejandro J. Castro

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  1. Victor Almeida
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  2. Jorge J. Betancor
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  3. Alejandro J. Castro
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Correspondence to Victor Almeida.

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Communicated by Markus Haase.

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Almeida, V., Betancor, J.J. & Castro, A.J. UMD Banach spaces and the maximal regularity for the square root of several operators. Semigroup Forum 88, 21–51 (2014). https://doi.org/10.1007/s00233-013-9498-3

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