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- W2950273211 abstract "Let X be a UMD space with type t and cotype q, and let T be a Fourier multiplier operator with a scalar-valued symbol m. If the Mihlin multiplier estimate holds for all partial derivatives of m up to the order n/max(t,q')+1, then T is bounded on the X-valued Bochner spaces. For scalar-valued multipliers, this improves the theorem of Girardi and Weis (J. Funct. Anal., 2003) who required similar assumptions for derivatives up to the order n/r+1, where r is a Fourier-type of X. However, the present method does not apply to operator-valued multipliers, which are also covered by the Girardi-Weis theorem." @default.
- W2950273211 created "2019-06-27" @default.
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- W2950273211 date "2009-09-17" @default.
- W2950273211 modified "2023-09-27" @default.
- W2950273211 title "New thoughts on the vector-valued Mihlin-Hormander multiplier theorem" @default.
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