Operator–valued Fourier multiplier theorems and maximal $L_p$-regularity
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 \(T_t\).
KeywordsFourier Multiplier Function Fourier Multiplier Multiplier Theorem Essential Assumption
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