Corrections to the Bjorken and Voloshin sum rules

We calculate near zero recoil the order alpha(s) corrections to the Bjorken and Voloshin sum rules that bound the B-->D(*)l<(nu)over bar> form factors. These bounds are derived by relating the result of inserting a complete set of physical states in a time-ordered product of weak currents to the operator product expansion. The sum rules sum over physical states with excitation energies less than a scale Delta. We find that the corrections to the Bjorken bound are moderate, while the Voloshin bound receives sizable corrections enhanced by Delta/Lambda(QCD). With some assumptions, we find that the slope parameter for the form factor h(A1) in B-->D*l<(nu)over bar> decay satisfies 0.4 less than or similar to rho(A1)(2) less than or similar to 1.3.