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Archiv der Mathematik

, Volume 82, Issue 5, pp 404–414 | Cite as

Operator-valued Fourier multiplier theorems on L p -spaces on \( \mathbb{T}^d \)

  • S. BuEmail author
  • J.-M. KimEmail author
Original paper

Abstract.

We establish operator-valued Fourier multiplier theorems on L p -spaces on \( \mathbb{T}^d \). The conditions on the multipliers depend on the geometry of the underlying Banach spaces (UMD property and property \( (\alpha)) \) and the growth rate (estimated by means of R-boundedness) at infinity of the partial derivatives of the multipliers. We also give an application of the obtained Fourier multiplier theorems to L p -maximal regularity for a second order problem.

Mathematics Subject Classification (2000):

42A45 42B15 46B20 46E40. 

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Copyright information

© Birkhäuser-Verlag 2004

Authors and Affiliations

  1. 1.Department of Mathematical ScienceUniversity of TsinghuaBeijingChina
  2. 2.Department of MathematicsUniversity of Kim II sungDPR Korea
  3. 3.Current Address: Department of Mathematical ScienceUniversity of TsinghuaBeijingChina

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