【摘 要】
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Let X, Y be UMD-spaces that have property (α), I ＜ p ＜∞ and let M be an R-bounded subset in ( )(X,Y). It is shown that {T(Mk)k∈z : Mk,k(Mk+1 - Mk) ∈M for k ∈
【机 构】
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Department of Mathematical Sciences
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Let X, Y be UMD-spaces that have property (α), I ＜ p ＜∞ and let M be an R-bounded subset in ( )(X,Y). It is shown that {T(Mk)k∈z : Mk,k(Mk+1 - Mk) ∈M for k ∈ Z} is an R-bounded subset of ( )(Lp(0, 2π; X), Lp(0, 2π; Y)), where T(Mk)k∈z denotes the Lp-multiplier given by the sequence (Mk)k∈z. This generalizes a result of Venni [10]. The author uses this result to study the strongly Lp-well-posedness of evolution equations with periodic boundary condition. Analogous results for operatorvalued Lp-multipliers on R are also given.
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