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Quantum mechanical uncertainty relations for position and momentum areexpressed in the form of inequalities involving the Renyi entropies. The proofof these inequalities requires the use of the exact expression for the(p,q)-norm of the Fourier transformation derived by Babenko and Beckner.Analogous uncertainty relations are derived for angle and angular momentum andalso for a pair of complementary observables in N-level systems. All theseuncertainty relations become more attractive when expressed in terms of thesymmetrized Renyi entropies

Formulation of the uncertainty relations in terms of the Rényi entropies