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On operator-valued Fourier multiplier theorems

Author(s): Zeljko Strkalj; Lutz Weis
Journal: Trans. Amer. Math. Soc. 359 (2007), 3529-3547.
MSC (2000): Primary 42B15, 42A45, 46E40; Secondary 46B09
Posted: March 20, 2007
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Abstract: The classical Fourier multiplier theorems of Marcinkiewicz and Mikhlin are extended to vector-valued functions and operator-valued multiplier functions on $ \mathbb{Z}^d$ or $ \mathbb{R}^d$ which satisfy certain $ R$-boundedness conditions.

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Additional Information:

Zeljko Strkalj
Affiliation: Institute of Mathematics I, University of Karlsruhe, Englerstrasse 2, D-76128 Karlsruhe, Germany
Email: zeljko.strkalj@math.uni-karlsruhe.de

Lutz Weis
Affiliation: Institute of Mathematics I, University of Karlsruhe, Englerstrasse 2, D-76128 Karlsruhe, Germany
Email: lutz.weis@math.uni-karlsruhe.de

DOI: 10.1090/S0002-9947-07-04417-0
PII: S 0002-9947(07)04417-0
Received by editor(s): October 1, 1999
Received by editor(s) in revised form: April 10, 2003
Posted: March 20, 2007
Copyright of article: Copyright 2007, American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.

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