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 \(T_t\).
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Received July 19, 1999 / Revised July 13, 2000 / Published online February 5, 2001
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Weis, L. Operator–valued Fourier multiplier theorems and maximal $L_p$-regularity. Math Ann 319, 735–758 (2001). https://doi.org/10.1007/PL00004457
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DOI: https://doi.org/10.1007/PL00004457