Holder inequalities and bounds on the masses of light quarks

QCD Laplace sum-rules must satisfy a fundamental (Holder) inequality if the y are to consistently represent an integrated hadronic cross-section. After subtraction of the pion-pole, the Laplace sum-rule of pion currents is sho wn to violate this fundamental inequality unless the u and d quark masses ( respectively denoted by m(u) and m(d)) are sufficiently large, placing a lo wer bound on the 1 eV <(MS)over bar> running masses. (C) 1999 Elsevier Scie nce B.V. All rights reserved.