LetX,YbeUMD-spacesthathaveproperty(α),I＜p＜∞andletMbeanR-boundedsubsetin()(X,Y).Itisshownthat{T(Mk)k∈z:Mk,k(Mk+1-Mk)∈Mfork∈Z}isanR-boundedsubsetof()(Lp(0,2π;X),Lp(0,2π;Y)),whereT(Mk)k∈zdenotestheLp-multipliergivenbythesequence(Mk)k∈z.ThisgeneralizesaresultofVenni[10].TheauthorusesthisresulttostudythestronglyLp-well-posednessofevolutionequationswithperiodicboundarycondition.AnalogousresultsforoperatorvaluedLp-multipliersonRarealsogiven.
