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Let (X(Rd),|.|X) be a normed space of real functions on Rd.Let >0 and Pα be the operator in X(Rd) defined by Pα f(x)=χα(x) f(x) (where χα(x) is thecharacteristic function of the cube Idα=[-α,α]d). Let L be asubspace of X(Rd). Set PαL=Pα f:f∈L. Suppose