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

Víctor Almeida; Jorge J. Betancor; Alejandro J. Castro

doi:10.1007/s00233-013-9498-3

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

Classical Analysis and ODEs 2023-10-25 v2

Authors: Víctor Almeida , Jorge J. Betancor , Alejandro J. Castro

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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 $L^2(\Omega, d\mu; X),$ characterizes the UMD property for the Banach space $X$ .

Keywords

UMD Banach spaces maximal $L^p$-regularity square root of operators Hermite operators Bessel operators Laguerre operators Cauchy problems

Cite

@article{arxiv.1209.5234,
  title  = {UMD Banach spaces and the maximal regularity for the square root of several operators},
  author = {Víctor Almeida and Jorge J. Betancor and Alejandro J. Castro},
  journal= {arXiv preprint arXiv:1209.5234},
  year   = {2023}
}

Comments

23 pages. To appear in Semigroup Forum

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