Weighted Uncertainty Principles in L∞ Original Research Article

We determine sufficient conditions on positive weights W and V such that there exists continuous, strictly increasing functions Φ and Ψ on [0, ∞) such that Φ(0)=0=Ψ(0) andΦ‖Wf‖∞|f̂(0)| Ψ ‖Vf̂‖∞|f(0)|⩾1 whenever f: R→R is a continuous integrable function. We also give an example that shows the optimality of our conditions.