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Mathematische Annalen

, Volume 319, Issue 4, pp 735–758 | Cite as

Operator–valued Fourier multiplier theorems and maximal $L_p$-regularity

  • Lutz Weis
Original article

Abstract.

We prove a Mihlin–type multiplier theorem for operator–valued multiplier functions on UMD–spaces. The essential assumption is R–boundedness of the multiplier function. As an application we give a characterization of maximal \(L_p\)–regularity for the generator of an analytic semigroup \(T_t\) in terms of the R–boundedness of the resolvent of A or the semigroup \(T_t\).

Keywords

Fourier Multiplier Function Fourier Multiplier Multiplier Theorem Essential Assumption 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2001

Authors and Affiliations

  • Lutz Weis
    • 1
  1. 1.Mathematisches Institut I, Universität Karlsruhe, 76128 Karlsruhe, Germany (e-mail: Lutz.Weis@math.uni-karlsruhe.de) DE

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