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On operator-valued Fourier multiplier theorems
Authors:Zeljko Strkalj  Lutz Weis
Institution:Institute of Mathematics I, University of Karlsruhe, Englerstrasse 2, D-76128 Karlsruhe, Germany ; Institute of Mathematics I, University of Karlsruhe, Englerstrasse 2, D-76128 Karlsruhe, Germany
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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